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In this paper, the extended finite element method (X-FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness-dominated regime of propagation and the so-called 2/3 asymptote in fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all. The method is thus very computationally effective and accurate as shown in previous related studies. This paper presents a further development of the BCM for multi-region problems in 2-D elasticity, and an application of this development, coupled with the displacement correlation technique, to evaluating the stress intensity factors K1 and K2 for bimaterial interface cracks. Some preliminary tests conducted within this work suggest that the proposed technique is robust and able to provide highly accurate results of both K1 and K2 for this challenging class of fracture problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Pyramidal elements are necessary to effect the transition from tetrahedral to hexahedral elements, a common requirement in practical finite element applications. However, existing pyramidal transition elements suffer from degeneracy or other numerical difficulties, requiring, at the least, warnings and care in their use. This paper presents a general technique for the construction of nodal basis functions on pyramidal finite elements. General forms for basis functions of arbitrary order are presented. The basis functions so derived are fully conformal and free of degeneracy. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for analysis of periodic oscillations of forced elastic systems with geometric nonlinearity is presented in this paper. Modal decomposition of the solution, computation of periodic oscillations for every eigenmode and estimation of geometric nonlinearities using the method of initial deformations enable to construct a computational technique that can be very effective in computation of steady-state periodic motions of slightly damped structures under periodic forcing. It is shown that the developed algorithm can be successfully exploited for the calculation of structural response of a micromechanical cantilever. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present work is inspired by Anderson et al. (Phys. D Nonlinear Phenom. 2000; 135(1–2):175–194) and Noll (http://www.math.cmu.edu/wn0g/noll) and falls in the conceptual line of the Ginzburg–Landau class of first-order phase-transition models based on the concept of phase-field parameter. Trying to keep the exposition as much general as possible, we develop below a thermodynamically consistent rationalization of the physical process of (anisotropic) deposition of pyrolytic carbon from a gas phase. The derivation line we follow is well established in the field of the modern continuum physics. From the covariance of the first principle of thermodynamics, the second Newton's law and the Liouville's theorem with respect to the one-dimensional Lie groups of transformations, the balance laws for the temperature, linear momentum and density are formulated. This system of partial differential equations is comprehended further by the constitutive laws for the phase field, the stress, and the heat and entropy fluxes obtained in a form consistent with the Clausius–Duhem understanding of the second law. The result referred to as a local, strongly coupled initial boundary value problem of chemical vapor deposition (IBVP-CVD) constitutes the general mathematical description of the CVD process. The weak form of isotropic IBVP-CVD is then derived and discretized by means of the discontinuous Galerkin method. At the end of the paper, we also derive the weak formulations for the local lifting operators that provide the stabilization mechanism for the discontinuous Galerkin discretization scheme. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid-Trefftz four-node quadrilateral element model is formulated for Helmholtz problem. In this model, two Helmholtz approximations are defined. The first approximation is obtained by nodal interpolation, and the second approximation is truncated from a Trefftz solution set. A hybrid variational functional is employed to enforce the equality of and other necessary conditions on the two approximations. From the numerical tests, it can be seen that the hybrid model is markedly more accurate than the conventional finite element model. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed-ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The subject of this paper is the calculation of charge distribution on the surfaces of thin conducting microelectromechanical systems beams, of nearly square cross-section, in electrostatic problems, by the boundary element method (BEM). A line model of a beam is proposed here. This model overcomes the problem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a numerical analysis to study thermal radiation effect on magnetohydrodynamic (MHD) unsteady mixed-convection flow over a moving vertical cylinder with constant heat flux through a porous medium in the presence of transversal uniform magnetic field has been performed. The boundary layer equations are transformed into a linear algebraic system by a Crank–Nicolson type of implicit finite-difference method. The stability condition of the scheme was studied. Numerical results are presented with various sets of parameters for both air and water. The results show many interesting effects on velocity, temperature and concentration profiles on local as well as average shear stress, rate of heat and mass transfer. Also, the velocity and temperature profiles are compared with the available results in the literature and it is found to be in good agreement. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a new Chebyshev-type method free from second derivative. An analysis of convergence shows that the new method has fourth-order convergence. Per iteration, the method requires one evaluation of the function and two of its first derivative and therefore this method has the efficiency index equal to 1.587. Numerical examples show that the method has definite practical utility. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the exact integration of discontinuous quadratic element for boundary element analysis of two-dimensional potential problems. It is proved by the mathematical induction that singular integral in Cauchy principal value (CPV) and hypersingular integral in Hadamard finite part (HFP) need no special treatment with the derived exact integration for discontinuous quadratic element. The evaluation of CPV and HFP without special treatment leads to an easy way to compute the potential and flux on the boundary. The differences of the recovered flux and those by solving algebraic equation at collocation points are interpolated as error indicator for adaptive boundary element analysis. Two numerical examples are given to verify the correctness of the exact integration and the feasibility of the proposed error indicator. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Crack propagation in concrete structures is a very complicated process, and the distribution of cracks may significantly affect the behaviour of the structures under time-dependent loading. If enough damage or extensive cracks exist in a structure, strengthening or repair using external carbon fibre-reinforced polymer (CFRP) reinforcement may be needed. Therefore, an understanding of the influence of the CFRP strengthening system on behaviour is crucial for the proper design of a structural reinforcement strategy. In this paper, we compare three major methods: the discrete crack method, the smeared crack method and the element-free method. By using these methods to study the fracture pattern of a beam with dapped ends, we can compare the capabilities and efficiencies of the three methods. When modelling the crack formation in reinforced concrete structures, the smeared crack approach gives better results than the discrete model in terms of crack spacing and regularity, however, it does not follow the crack growth well. The element-free Galerkin method seems to be superior to the other methods in the sense that it deals with the irregular cracks well and is very efficient in saving computing time. The preferred choice of method depends on the type of problem and the solution accuracy required, and this also depends on a certain balance between the accurate tracing of individual cracks and the computing efficiency. In addition, new algorithms are required for the efficient simulations of dynamic crack propagation, especially in the case of pre-cracked structures strengthened with prestressed CFRPs. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stabilization method for the Stokes problem, using equal-order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal-order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well-known idea of using mass lumping as a stabilization mechanism. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an explicit form for the numerical solution of problems in the space–time domain by using quadrature rules is proposed. The compact form of the shape functions recently proposed by the author is useful to the scope. Numerical solutions for the time-dependent one-dimensional nonlinear heat conduction problem are calculated by means of the iterative differential quadrature method, a method proposed by the author and based on quadrature rules. The accuracy of the solution and stability analysis show good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents simple time domain fundamental solutions for the three-dimensional (3D) well known u–p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Simulation of multiphysics problems is a common task in applied research and industry. Often a multiphysics solver is built by connecting several single-physics solvers into a network. In this paper, we develop a basic adaptive methodology for such multiphysics solvers. The adaptive methodology is based on a posteriori error estimates that capture the influence of the discretization errors in the different solvers on a given functional output. These estimates are derived using duality-based techniques. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix–Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Least-squares finite-element methods for Darcy flow offer several advantages relative to the mixed-Galerkin method: the avoidance of stability conditions between finite-element spaces, the efficiency of solving symmetric and positive definite systems, and the convenience of using standard, continuous nodal elements for all variables. However, conventional C0 implementations conserve mass only approximately and for this reason they have found limited acceptance in applications where locally conservative velocity fields are of primary interest. In this paper, we show that a properly formulated compatible least-squares method offers the same level of local conservation as a mixed method. The price paid for gaining favourable conservation properties is that one has to give up what is arguably the least important advantage attributed to least-squares finite-element methods: one can no longer use continuous nodal elements for all variables. As an added benefit, compatible least-squares methods inherit the best computational properties of both Galerkin and mixed-Galerkin methods and, in some cases, yield identical results, while offering the advantages of not having to deal with stability conditions and yielding positive definite discrete problems. Numerical results that illustrate our findings are provided. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a numerical approach for examining a spherically symmetric advective–dispersive contaminant transport problem. The Taylor–Galerkin method that is based on an Euler time-integration scheme is used to solve the governing transport equation. A Fourier analysis shows that the Taylor–Galerkin method with a forward Euler time integration can generate an oscillation-free and non-diffusive solution for the pure advection equation when the Courant number satisfies the constraint Cr = 1. Such numerical advantages, however, do not extend to the advection–dispersion equation. Based on these observations, an operator-splitting Euler-integration-based Taylor–Galerkin scheme is developed to model the advection-dominated transport process for a problem that exhibits spherical symmetry. The spherically symmetric transport problem is solved using this approach and a conversion to a one-dimensional linear space with an associated co-ordinate transformation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The method proposed by J.C. Houbolt in 1950 is one of the pioneering methods of time integration. Nevertheless, especially due to its multi-step fashion and not having a well-defined starting procedure, the method has not met considerable acceptance. The conversion of the Houbolt method to a one-step method is reported in the literature. However, the resulting method still lacks an appropriate starting procedure for all practical cases. In this paper, a parameter-less unified starting procedure is proposed for time integration with the Houbolt method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831–847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge–Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The quadrilateral area co-ordinate (QAC) method is a new tool for developing quadrilateral finite element models. Compared with those traditional elements using isoparametric co-ordinates, models formulated by QAC method are less sensitive to mesh distortion. Furthermore, another advantage for QAC system is that the analytical expressions for element stiffness matrix can be obtained theoretically by basic formulae of QAC integrals, which are beneficial to finite element computation procedure. However, because of the relative complexity of the derivation process, no such explicit form of the stiffness matrix has been presented before. In this paper, the analytical element stiffness matrix of a recent 4-node quadrilateral membrane element, AGQ6-I, is given out for the first time. This element AGQ6-I, which was constructed by QAC method and generalized conforming conditions, successfully overcomes various locking problems and exhibits much better performances than many isoparametric models. And its formulations have also been introduced in shell analysis by other researchers. Numerical examples show that obvious higher computation efficiency can be achieved by presented explicit formulations. So the analytical form of the element stiffness matrix of element AGQ6-I possesses significance for its further applications. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a systematic numerical analysis for a mixed nonlinear model of shock absorber under vibration excitation. The mixed nonlinear model is presented for attenuating vibration by considering the coupling of quadratic damping, viscosity damping, Coulomb damping and nonlinear spring forces. An approximate computational analytical solution for the dynamic transmissibility of the shock absorber was deduced by combining Fourier transforms and the harmonic balance method with deterministic excitation. The mathematical characteristics of the dynamic transmissibility were analyzed to illustrate the dynamic performance of the shock absorber. The results show multiple solutions, especially the low-frequency attenuation characteristics below the resonance frequency. The results provide a theoretical basis for the design of nonlinear shock absorbers. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix–vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the preliminary results of an extensive numerical parametric study on seismic behaviour of two-dimensional semi-sine-shaped valleys subjected to vertically propagating incident in-plane compression and shear waves. The medium is assumed to have a linear elastic constitutive behaviour. All calculations are executed in time-domain using the direct boundary element method. Clear perspectives of the amplification patterns of the valley are presented by investigation of the frequency-domain responses. It is shown that wavelength, site geometry and in a less order of importance, wave type and material parameters, are the independent key parameters governing the valley's amplification pattern. Some simple rules are obtained which could be used in seismic microzonation and seismic design of structures founded inside the valley. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier–Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171–186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199–210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a stabilized space–time Petrov–Galerkin finite element model of coastal ocean circulation is derived. Continuous linear interpolation in space and time is employed and a spatial unstructured mesh of triangular elements is used. To simulate the hydro-thermodynamical ocean behaviour a gravity reduced model is proposed. This model solves the motion and continuity hydrodynamic equations coupled with the advection–diffusion transport equation for temperature which governs the heat exchanges in the upper layer. The model is used to evaluate the main dynamical features of the coastal waters of the Rio de Janeiro State, namely: cold plumes, coastal jets and the influence of the warmer water bays. Numerical experiments are performed to highlight the typical observed events of coastal upwelling phenomena and their interaction with the existing coastal bays and the offshore conditions. Such experiments deal with a series of idealized northeast wind field forcing patterns, showing the solutions dependence on the horizontal structure of the wind fields in relation to the coastline configuration. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present the construction and computational assessment of an hp-version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier–Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, which ensures that the incompressibility constraint is automatically satisfied, we reduce the system of Navier–Stokes equations to a single fourth-order nonlinear partial differential equation. We introduce a discretization of this fourth-order nonlinear partial differential equation based on a combination of the symmetric DGFEM for the biharmonic part of the equation and a DGFEM with jump-penalty terms for the hyperbolic part of the problem, and then we solve the resulting nonlinear problem using Newton's method. Numerical examples, including the solution of the 2D lid-driven cavity flow problem, are presented to demonstrate the convergence and accuracy of the method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A computational modelling for the prediction of the hydrodynamic performance of a centrifugal pump in cavitating flows is presented in this paper. The cavitation model is implemented in a viscous Reynolds-averaged Navier–Stokes solver. The cavity interface and shape are determined using an iterative procedure matching the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient on the wall, is taken into account in updating the cavity shape iteratively. Numerical validation of the present cavitation model and algorithms is performed on different headform/cylinder bodies for a range of cavitation numbers through comparing with the experimental data. Flow characteristics trends associated with off-design flow and twin cavities in the blade channel are observed using the presented cavitation prediction. The rapid drop in head coefficient at low cavitation number is captured for two different flow coefficients. Local flow field solution illustrates the principle physical mechanisms associated with the onset of breakdown. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new method for computing eigenvector derivatives with distinct and repeated eigenvalues for the real symmetric eigensystems is presented. Its main idea is to extend the governing equations of particular solutions for eigenvector derivatives. The extension is completed by requiring the solution to be mass orthogonal with respect to the distinct or repeated modes and adjusting the corresponding coefficients so that the coefficient matrix of the extended system is non-singular and has smaller condition number. Numerical examples are included to demonstrate the validity of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper describes the application of the primal-dual theory of limit and shakedown analysis in safety assessment and design of pressure components according to the new European approach to design by analysis. Two methods, the static and kinematic one, and their combination, the primal-dual method, are discussed. A numerical example is presented to show the robustness of the primal-dual method compared with two other methods recently used in two European projects on safety assessment and design. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A simplified method for analysing lateral response of suspension bridges under wind loads is proposed in this paper. The geometric non-linearity in the deflection theory and the three components of displacement-dependent wind loads are taken into account in the method. The analytical formulas for calculating the torsional, vertical, and lateral responses of suspension bridges under wind loads are derived. An iterative procedure, which has a high convergence rate for solving the problem, is developed. The proposed method is sufficient and simple to use. Wind-induced lateral response analysis of a long-span suspension bridge demonstrates the proposed method's efficiency and accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We develop a numerical method to solve $$L_{\varepsilon} u_{\varepsilon} =- {{\partial} \over {\partial x_{i}}} a_{ij} (x / \varepsilon ) {{\partial} \over {\partial x_{j}}} u_{\varepsilon} = f \quad {\rm in} \, \, \Omega, \quad u_{ \varepsilon} =0 \quad {\rm on} \, \, \partial \Omega $$ where the matrix a(y)=(aij(y)) is symmetric positive definite, whose entries are periodic functions of y with periodic cell Y. More specifically we assume $ a_{ij} \in C^{1, \beta} (\Re^{2}), \quad \beta > 0 $. It is also assumed that there exists positive constants γa and βa such that $ \gamma_{a} ||\xi ||^{2} \le a_{ij} (y) \xi_{i} \xi_{j} \le \beta_{a} ||\xi||^{2} $ for all $ \xi \in \Re^{2} $ and $ y \in {\bar Y} $. The major goal in this paper is to develop a numerical approximation scheme on a mesh size h > ℇ (or h≫ℇ) with quasi-optimal approximation on L2 and broken H1 norms. The new method is based on asymptotic analysis and a careful treatment of the boundary corrector term. This kind of equation has applications in areas such as the study of flow through porous media and composite materials. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper reports on the non-linear static analysis of 2D concrete structures using an hybrid-mixed stress formulation and continuum damage mechanics. The finite element model adopted is based on the direct and independent approximation of three fields: the effective stress and displacement fields in the domain of each element and the displacement field on the static boundary. The non-linear behaviour of the material is modelled with a non-local isotropic damage model. A set of numerical examples are presented to illustrate and validate the use of such numerical technique. The performance of the model is assessed by comparison with results obtained using other numerical schemes presented in the literature and also with experimental results. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper reports a new Chebyshev spectral collocation method for directly solving high-order ordinary differential equations (ODEs). The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows the multiple boundary conditions to be incorporated more efficiently. Numerical results show that the proposed formulation significantly improves the conditioning of the system and yields more accurate results and faster convergence rates than conventional formulations. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We developed in this paper a variational formulation of heat diffusion equation applicable to the flat shell context and cellular structures. For this purpose, we introduce the average mid-surface temperature field, through-the-thickness gradient and their dual generalized fluxes. Moreover, we introduced radiative heat exchange in the same way, which leads to a non-linear and unsymmetrical thermal discrete problem. The model performance is illustrated by several numerical examples concerning cellular structures like hollow clay bricks submitted to thermal loading. Thermo-mechanical coupling for such structure which is well adapted to the shell-like modelling approach, is presented in the elastic regime with the numerical results concerning temperature field and forces. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the discontinuous Galerkin (DG) finite element method is applied to simulate high-temperature equilibrium airflows. Two approximate Riemann solvers are used to compute the advective flux. A second-order TVD Runge–Kutta time integration scheme is employed to march the solution in time. The extension to equilibrium chemistry is implemented by using the effective &gamma approach. The effective &gamma is obtained through a polynomial curve fit. With this approach, the computation of the species composition of the equilibrium air can be completely separated from the main solver. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the DG method in chemically reacting airflows. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Unstructured mesh based discretization techniques can offer certain advantages relative to standard finite difference approaches which are commonly used in reservoir simulation, due to their flexibility to model complex geological features and to their ability to easily incorporate mesh adaptation. Within such class of methods the most frequently used are the finite element method (FEM) and the finite volume method (FVM). The latter is particularly attractive in reservoir problems due to its local and global conservation properties. The main goal of the present paper is to describe an unstructured edge-based FVM formulation which is used to solve the partial differential equations resulting from the modelling of two-phase fluid flow of oil and water in homogeneous porous media, when an IMPES (IMplicit Pressure Explicit Saturation) approach is used. This finite volume formulation is similar to the edge-based FEM formulation when linear triangular or tetrahedral elements are employed. Some model examples are presented in order to validate the presented formulation. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a rotation-free, subdivision-based, isoparametric quadrilateral finite element for the analysis of doubly-curved thin shells. The element is a generalization of spline-based C1 finite elements to curved domains, and general mesh connectivity. It uses semi-local basis functions that span the two-neighbourhood of a node. The traditional difficulty with this class of elements comes from the fact that these basis functions depend on the valence of the nodes of the element. For elements with 4-valence nodes the basis functions are bicubic polynomials, but there are no simple closed-form expressions for them when the nodes have general connectivity patterns. In the paper, we show how the basis functions for the general case may be efficiently evaluated as linear combinations of translation and scaling transformations of the bicubic polynomials. The performance of the resulting element is illustrated on a hemispherical shell model problem. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An efficient and accurate locking-free corotational beam finite element for the analysis of large displacements and small-strain problems is developed in this paper. Three different finite element models based on three different beam theories, namely, the Euler–Bernoulli, Timoshenko, and simplified Reddy theories are presented. In order to develop a single corotational finite element that incorporates the kinematics of all three theories, the unified linear finite element model of beams developed by Reddy (Comm. Numer. Meth. Eng. 1997; 13:495–510) is included in the formulation. An incremental iterative technique based on the Newton–Raphson method is employed for the solution of the non-linear equilibrium equations. Numerical examples that demonstrate the efficiency and large rotation capability of the corotational formulation are presented. The element is validated by comparisons with exact and/or approximate solutions available in the literature. Very good agreement is found in all cases. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for generating multi-resolution adaptive triangulations of non-manifold 3D objects composed of several regions with arbitrary geometry. The process first immerses the input boundary elements inside a semi-regular adaptive tetrahedral mesh known as a BMT triangulation. The mesh elements are then pushed towards the boundary by means of a physically based compression scheme, more specifically, a mass-spring system. The final triangulation has no degenerated tetrahedra and provides an approximation of the boundary based on a chosen resolution. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, incorporating the hybrid method and the mixed interpolation method into a unified optimization framework, a 4-node quadrilateral plate element with bilinear displacement approximations is proposed. By an energy optimization tactic, among all of assumed linear bending moment modes, a 5-parametric optimal bending moment mode is selected. Using the optimal bending moment mode to improve the well-known plate element MITC4, the optimized plate element numerically possesses high accuracy at the coarse meshes in the analysis of thin/thick plates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well known that conforming finite element schemes exhibit Poisson locking in the incompressible limit as the Poisson ratio ν tends to 1/2. A remedy for this is to use a non-conforming method (Math. Comput. 1992; 59:321-328) in which an a priori error bound is proved for the Crouzeix–Raviart scheme. In this paper we derive a new a priori estimate for the error in energy for the Fortin–Soulie finite element method using a method similar to that used in Brenner and Sung. We then illustrate the new error bound by presenting some numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Imposition of essential boundary conditions in meshfree methods is made difficult because the shape functions used do not possess the ‘delta’ property. Various procedures have been proposed including penalty, Lagrange multipliers and collocation. It is shown in this paper that the success of a procedure depends on the arrangement of the nodal points. Certain methods of imposing boundary conditions are shown not to work for unstructured nodal arrangements. Much previous work has been demonstrated using structured grids thus hiding these drawbacks. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–diffusion problems. The discretization in time is performed before the spatial discretization by introducing second- and third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage of the wavelet bases capabilities to compress both functions and operators are presented. Numerical examples demonstrate the efficiency of our approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281–4298; 4299–4312; 4313–4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. &Deltat⩽4κ/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In variational and optimization problems where the field variable is represented by a series of functions that individually do not satisfy the constraints, penalty functions are often used to enforce the constraint conditions approximately. The major drawback with this approach is that the error due to any violation of the constraint is not known. In a recent publication dealing with the Rayleigh–Ritz method it was shown that, by using a combination of positive and negative penalty parameters, any error due to the violation of the constraints may be kept within any desired tolerance. This paper shows that this approach may also be used in solving partial differential equations using a Galerkin's solution to Laplace's equation subject to mixed Neumann and Dirichlet boundary conditions as an example. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a finite element solution algorithm for the numerical solution of large size three-dimensional flow problems on a personal computer. To demonstrate the algorithm, the Stokes equations in velocity–vorticity form are solved for a lid-driven cubical cavity problem. The Galerkin's weighted residual form of the governing equations is evaluated for all the elements of the computational domain and kept as element-matrices and element-vectors. This results in a set of simultaneous equations corresponding to the global nodes of each element. Those elements that contain the boundary nodes are modified to incorporate the Dirichlet boundary conditions. A conjugate gradient iterative scheme is employed to solve the simultaneous equations in element form to get the solution at the global nodes. The matrix–vector products used in the conjugate gradient iterative solver are performed in element level, assembling only the element-level vectors to form the global vectors. Since the element-level computation has eluded the formation of global matrices, the numerical solution of three-dimensional Stokes equations using a mesh of size as high as 513 could be achieved on a personal computer. The algorithm is validated by comparing the results for a three-dimensional transient diffusion problem and Stokes flow in a lid-driven cubical cavity. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]