Some error estimates for the lumped mass finite element method for a parabolic problem
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- by P. Chatzipantelidis, R. D. Lazarov and V. Thomée PDF
- Math. Comp. 81 (2012), 1-20 Request permission
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.References
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Additional Information
- P. Chatzipantelidis
- Affiliation: Department of Mathematics, University of Crete, GR–71409 Heraklion, Greece
- Email: chatzipa@math.uoc.gr
- 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
- Email: lazarov@math.tamu.edu
- 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
- Email: thomee@chalmers.se
- Received by editor(s): November 5, 2009
- Received by editor(s) in revised form: November 2, 2010
- Published electronically: May 23, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1-20
- MSC (2010): Primary 65M60, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-2011-02503-2
- MathSciNet review: 2833485