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

Handle URI:
http://hdl.handle.net/10754/599674
Title:
Some error estimates for the lumped mass finite element method for a parabolic problem
Authors:
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
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. © 2011 American Mathematical Society.
Citation:
Chatzipantelidis P, Lazarov RD, Thomée V (2012) Some error estimates for the lumped mass finite element method for a parabolic problem. Math Comp 81: 1–20. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02503-2.
Publisher:
American Mathematical Society (AMS)
Journal:
Mathematics of Computation
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
1-Jan-2012
DOI:
10.1090/s0025-5718-2011-02503-2
Type:
Article
ISSN:
0025-5718; 1088-6842
Sponsors:
The research of R.D. Lazarov was supported in parts by US NSF Grants DMS-0713829, DMS-1016525, the Pichoridis Distinguished Lectureship through the Universityof Crete in 2008, and by award KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorChatzipantelidis, P.en
dc.contributor.authorLazarov, R. D.en
dc.contributor.authorThomée, V.en
dc.date.accessioned2016-02-28T06:07:15Zen
dc.date.available2016-02-28T06:07:15Zen
dc.date.issued2012-01-01en
dc.identifier.citationChatzipantelidis P, Lazarov RD, Thomée V (2012) Some error estimates for the lumped mass finite element method for a parabolic problem. Math Comp 81: 1–20. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02503-2.en
dc.identifier.issn0025-5718en
dc.identifier.issn1088-6842en
dc.identifier.doi10.1090/s0025-5718-2011-02503-2en
dc.identifier.urihttp://hdl.handle.net/10754/599674en
dc.description.abstractWe 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. © 2011 American Mathematical Society.en
dc.description.sponsorshipThe research of R.D. Lazarov was supported in parts by US NSF Grants DMS-0713829, DMS-1016525, the Pichoridis Distinguished Lectureship through the Universityof Crete in 2008, and by award KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST).en
dc.publisherAmerican Mathematical Society (AMS)en
dc.subjectError estimatesen
dc.subjectLumped mass methoden
dc.subjectNonsmooth initial dataen
dc.subjectParabolic partial differential equationsen
dc.titleSome error estimates for the lumped mass finite element method for a parabolic problemen
dc.typeArticleen
dc.identifier.journalMathematics of Computationen
dc.contributor.institutionPanepistimio Kritis, Rethymnon, Greeceen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionInstitute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgariaen
dc.contributor.institutionChalmers University of Technology, Göteborg, Swedenen
dc.contributor.institutionFoundation for Research and Technology-Hellas, Heraklion, Greeceen
kaust.grant.numberKUS-C1-016-04en
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