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Some error estimates for the lumped mass finite element method for a parabolic problem

Authors: P. Chatzipantelidis, R. D. Lazarov and V. Thomée
Journal: Math. Comp. 81 (2012), 1-20
MSC (2010): Primary 65M60, 65M15
Published electronically: May 23, 2011
MathSciNet review: 2833485
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Abstract: We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation. We also discuss the application to time discretization by the backward Euler and Crank–Nicolson methods.

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Additional Information

P. Chatzipantelidis
Affiliation: Department of Mathematics, University of Crete, GR–71409 Heraklion, Greece

R. D. Lazarov
Affiliation: Department of Mathematics, Texas A&M University, College Station, TX 77843, USA, and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
MR Author ID: 111240

V. Thomée
Affiliation: Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Göteborg, Sweden, and Institute of Applied and Computational Mathematics, FORTH, Heraklion GR–71110, Greece
MR Author ID: 172250

Keywords: Lumped mass method, parabolic partial differential equations, nonsmooth initial data, error estimates
Received by editor(s): November 5, 2009
Received by editor(s) in revised form: November 2, 2010
Published electronically: May 23, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.