*STOCHASTIC convergence, *LEAST squares, *FINITE element method, *APPROXIMATION theory, *FIXED point theory, *BOUNDARY value problems, *NUMERICAL analysis, *ERROR analysis in mathematics
Abstract
Abstract: In this paper, a least-squares finite element method for second-order two-point boundary value problems is considered. The problem is recast as a first-order system. Standard and improved optimal error estimates in maximum-norms are established. Superconvergence estimates at interelement, Lobatto, and Gauss points are developed. Numerical experiments are given to illustrate theoretical results. [Copyright &y& Elsevier]
*STOCHASTIC convergence, *FINITE element method, *BOUNDARY value problems, *APPROXIMATION theory, *ASYMPTOTIC expansions, *ERROR analysis in mathematics, *NUMERICAL analysis
Abstract
Abstract: In this paper, we investigate the superconvergence properties of the - version of the finite element method (FEM) for two-point boundary value problems. A postprocessing technique for the - finite element approximation is analyzed. The analysis shows that the postprocess improves the order of convergence. Furthermore, we obtain asymptotically exact a posteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis. [Copyright &y& Elsevier]