BDF-FEM for parabolic singularly perturbed problems with exponential layers on layer-adapted meshes in space

Authors:
Vit Dolejší;Hans-Görg Roos
Affiliations:
Faculty of Mathematics and Physics, Charles University Prague;Department of Mathematics, TU Dresden
Venue:
Neural, Parallel & Scientific Computations
Year:
2010

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Abstract

A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, for instance, a pure Galerkin technique or stabilizations with certain properties on a Shishkin-type mesh, with two-step backward differencing in time. We prove optimal robust error estimates and present numerical results.