TY - JOUR
T1 - Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems
AU - Franz , Sebastian
AU - Linß , Torsten
AU - Roos , Hans-Görg
AU - Schiller , Sebastian
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, Edge stabilization, FEM, Uniform convergence,
Shishkin mesh.
AB - <p style="text-align: justify;">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 $L_2$&nbsp;norm and opens the door to the application of postprocessing for improving the discrete solution.</p>