Title: Layer-adapted meshes and FEM for time-dependent singularly perturbed reaction-diffusion problems

Authors: T. Linss

Addresses: Institut fur Numerische Mathematik, Technische Universitat Dresden, Germany

Abstract: We consider a non-monotone FEM discretisation of a singularly perturbed time-dependent reaction-diffusion problem whose solution exhibits strong parabolic layers. We conduct a stability and convergence analysis for arbitrary meshes. The method is shown to be maximum-norm stable although it is not inverse monotone. The convergence result implies convergence of the method on Shishkin and Bakhvalov meshes uniformly in the perturbation parameter e. Numerical experiments complement our theoretical results.

Keywords: reaction-diffusion problems; FEM discretisation; layer-adapted meshes; singular perturbations; finite element method; parabolic layers; stability; convergence analysis; arbitrary meshes.

DOI: 10.1504/IJCSM.2007.016535

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.259 - 270

Published online: 07 Jan 2008 *

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