Volume 28, Issue 1
Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems

Torsten Linß, Hans-Görg Roos & Sebastian Schiller

J. Comp. Math., 28 (2010), pp. 32-44.

Published online: 2010-02

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  • 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 ||(pi)u-u^(h)||E where pi*u 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 L2 norm and opens the door to the application of postprocessing for improving the discrete solution.

  • Keywords

Convection-diffusion problems Edge stabilizaton FEM Uniform convergence

  • AMS Subject Headings

65N15 65N30 65N50.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-32, author = {}, title = {Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {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 ||(pi)u-u^(h)||E where pi*u 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 L2 norm and opens the door to the application of postprocessing for improving the discrete solution.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m1005}, url = {http://global-sci.org/intro/article_detail/jcm/8505.html} }
TY - JOUR T1 - Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems JO - Journal of Computational Mathematics VL - 1 SP - 32 EP - 44 PY - 2010 DA - 2010/02 SN - 28 DO - http://doi.org/10.4208/jcm.2009.09-m1005 UR - https://global-sci.org/intro/article_detail/jcm/8505.html KW - Convection-diffusion problems KW - Edge stabilizaton KW - FEM KW - Uniform convergence AB -

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 ||(pi)u-u^(h)||E where pi*u 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 L2 norm and opens the door to the application of postprocessing for improving the discrete solution.

Torsten Linß, Hans-Görg Roos & Sebastian Schiller. (2019). Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems. Journal of Computational Mathematics. 28 (1). 32-44. doi:10.4208/jcm.2009.09-m1005
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