Finite elements scheme in enriched subspaces for singularly perturbed reaction–diffusion problems on a square domain

Article type: Research Article

Authors: Jung, Chang-Yeol^;

Affiliations: The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA | Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA

Abstract: In this article, we discuss reaction-diffusion problems which produce ordinary boundary layers and elliptic corner layers. Using the classical polynomial Q1-finite elements spaces enriched with the so-called boundary layer elements which absorb the singularities due to the boundary and corner layers we are able to attain high numerical accuracies. We essentially obtain ε-uniform approximation errors in a weighted energy norm with significant simplifications in the numerical implementations; here we do not use mesh refinements.

Keywords: boundary layers, finite elements, singularly perturbed problem, reaction-diffusion, enriched subspaces

DOI: 10.3233/ASY-2008-0865

Journal: Asymptotic Analysis, vol. 57, no. 1-2, pp. 41-69, 2008