Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers
Numerical Analysis
2020-11-12 v1 Numerical Analysis
Abstract
We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost uniform convergence and superconvergence. The use of graded mesh allows for the SDFEM to prove almost uniform esimates in the SD norm, which is not possible for Shishkin type meshes.
Keywords
Cite
@article{arxiv.2011.05737,
title = {Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers},
author = {Mirjana Brdar and Goran Radojev and Hans-Görg Roos and Ljiljana Teofanov},
journal= {arXiv preprint arXiv:2011.05737},
year = {2020}
}