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

P. Chatzipantelidis; R. D. Lazarov; V. Thomée

doi:10.1090/s0025-5718-2011-02503-2

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

P. Chatzipantelidis, R. D. Lazarov, V. Thomée

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1-20
Number of pages	20
Journal	Mathematics of Computation
Volume	81
Issue number	277
DOIs	https://doi.org/10.1090/s0025-5718-2011-02503-2
State	Published - Jan 1 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Access to Document

10.1090/s0025-5718-2011-02503-2

Cite this

@article{bbcee278ad3444c391a3b24467fed87f,

title = "Some error estimates for the lumped mass finite element method for a parabolic problem",

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. {\textcopyright} 2011 American Mathematical Society.",

author = "P. Chatzipantelidis and Lazarov, {R. D.} and V. Thom{\'e}e",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2012",

month = jan,

day = "1",

doi = "10.1090/s0025-5718-2011-02503-2",

language = "English (US)",

volume = "81",

pages = "1--20",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "277",

}

TY - JOUR

T1 - Some error estimates for the lumped mass finite element method for a parabolic problem

AU - Chatzipantelidis, P.

AU - Lazarov, R. D.

AU - Thomée, V.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/599674

UR - http://www.ams.org/jourcgi/jour-getitem?pii=S0025-5718-2011-02503-2

UR - http://www.scopus.com/inward/record.url?scp=84858982073&partnerID=8YFLogxK

U2 - 10.1090/s0025-5718-2011-02503-2

DO - 10.1090/s0025-5718-2011-02503-2

M3 - Article

SN - 0025-5718

VL - 81

SP - 1

EP - 20

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 277

ER -

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

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this