Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes
Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 593–606
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, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $\theta$-scheme as for discontinuous Galerkin in time.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-740
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 593–606
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Convection-diffusion transient finite element Shishkin mesh time discretization.