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Abstract: In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5–10 is observed in all simulations. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we study the superconvergence of the frictionless Signorini problem. When approximated by bilinear finite elements, by virtue of the information on the contact zone, we can derive a superconvergence rate of under a proper regularity assumption. Finally, a numerical test is given to verify our result. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the spatial and spectral superconvergence properties of one-dimensional hyperbolic conservation law by a discontinuous Galerkin (DG) method. The analyses combine classical mathematical arguments with MATLAB experiments. Some properties of the DG schemes are discovered using discrete Fourier analyses: superconvergence of the numerical wave numbers, Radau structure of the X spatial error. [Copyright &y& Elsevier]

Abstract: This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We show the numerical effects of loss of coercivity. [Copyright &y& Elsevier]

Abstract: The combined CFD-PBE (population balance models) are computationally intensive requiring efficient numerical methods for solving practical problems. In this paper, a high order method is presented based on the least-squares method (LSM) for the solution of a spatial-dependent population balance equation which includes advective processes. Numerical experiments are performed in order to study the behavior of the proposed method for one-dimensional cases using model problems with analytical solutions. [Copyright &y& Elsevier]

Abstract: In this paper we revisit the solution of ill-posed problems by preconditioned iterative methods from a Bayesian statistical inversion perspective. After a brief review of the most popular Krylov subspace iterative methods for the solution of linear discrete ill-posed problems and some basic statistics results, we analyze the statistical meaning of left and right preconditioners, as well as projected-restarted strategies. Computed examples illustrating the interplay between statistics and preconditioning are also presented. [Copyright &y& Elsevier]

Abstract: Graves-Morris (see [P.R. Graves-Morris, Vector valued interpolants I, Numer. Math. 42 (1983) 331–348 and P.R. Graves-Morris and C.D. Jenkins, Vector valued rational interpolants III, Constr. Approx. 2 (1986) 263–289]) defined the generalized inverse rational interpolants (GIRIs) in the form of with the divisibility condition , and proved the Uniqueness Theorem for GIRIs. However, this condition is found not necessary in some cases. In this paper, we remove this divisibility condition, define the extended generalized inverse rational interpolants (EGIRIs) and establish the Uniqueness Theorem for EGIRIs. One can see that the Uniqueness Theorem for GIRIs is the special case of the one for EGIRIs. [Copyright &y& Elsevier]

The authors found some errors in their above titled paper which should be corrected in this Corrigendum. [ABSTRACT FROM AUTHOR]