Superconvergence of the h-p version of the finite element method in one dimension

Authors:
Lijun Yi;Benqi Guo
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China and Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 11
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Abstract

In this paper, we investigate the superconvergence properties of the h-p version of the finite element method (FEM) for two-point boundary value problems. A postprocessing technique for the h-p 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.