Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems
Year: 2010
Author: Sebastian Franz, Torsten Linß, Hans-Görg Roos, Sebastian Schiller
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 32–44
Abstract
In the present paper the edge stabilization technique is applied to a convection-diffusion problem with exponential boundary layers on the unit square, using a Shishkin mesh with bilinear finite elements in the layer regions and linear elements on the coarse part of the mesh. An error bound is proved for ${||πu−u^h||}_E$ where $πu$ is some interpolant of the solution $u$ and $u^h$ the discrete solution. This supercloseness result implies an optimal error estimate with respect to the $L_2$ norm and opens the door to the application of postprocessing for improving the discrete solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.09-m1005
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 32–44
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Convection-diffusion problems Edge stabilization FEM Uniform convergence Shishkin mesh.