Layer-adapted meshes and FEM for time-dependent singularly perturbed reaction-diffusion problems
by T. Linss
International Journal of Computing Science and Mathematics (IJCSM), Vol. 1, No. 2/3/4, 2007

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.

Online publication date: Mon, 07-Jan-2008

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