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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 integrals required in the computation of influence coefficient matrices of the boundary element method (BEM) depend on the distance r(x,x′) from the collocation point or field point x to the source or load point x′. As a consequence, a distinction must be made between the case where the collocation point does not belong to the integration domain (proper integrals) and the case where the collocation point does belong to the integration domain (improper integrals). Moreover, situations arise where x comes close to x′ and the integrals, albeit of a regular character, behave almost as improper, this case being referred to as nearly singular integration. Analytical integration captures best the singular or nearly singular kernel behavior, but this technique can only be carried out in very simple situations as, for instance, boundary integrals over straight elements. In the present paper a set of useful analytical integration formulas for the 2D BEM with curved elements is deduced, employing a symbolic computational algebra system. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviors with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability. [ABSTRACT FROM AUTHOR]

In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the convergence and divergence rates for a class of generalized matrix multisplitting relaxation methods in a detailed manner. In particular, when the coefficient matrix is an L-matrix, I obtain several sufficient and necessary conditions ensuring the convergence of these methods. [ABSTRACT FROM AUTHOR]

In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher- order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for elements, not for nodes. An 'element patch', which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. [ABSTRACT FROM AUTHOR]

The paper deals with the solution of the quasi-harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient. [ABSTRACT FROM AUTHOR]

The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non-linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive-definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion [ABSTRACT FROM AUTHOR]

This paper compares two formulations of Lax-Wendroff TVD methods. The basis of comparison is to the results of several test problems providing both qualitative and quantitative results. Results show that using an upwind biased limiter provides higher resolution of both smooth and discontinuous solutions from a lower amount of induced numerical viscosity. The conclusion is that a limiter should have as small a support as possible in order to limit its effects if high resolution is the object. [ABSTRACT FROM AUTHOR]