Maximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs

Messaoud Boulbrachene, Qais Al Farei

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of the geometrical convergence of both the continuous and corresponding discrete Schwarz sequences. We also give some numerical results to support the theory.

Original languageEnglish
Pages (from-to)21-29
Number of pages9
JournalApplied Mathematics and Computation
Volume238
DOIs
Publication statusPublished - Jul 1 2014

Fingerprint

Non-matching Grids
Elliptic PDE
Maximum Norm
Domain Decomposition
Finite Element Approximation
Error Analysis
Error analysis
Finite Element Method
Decomposition
Converge
Finite element method
Numerical Results
Approximation
Context

Keywords

  • Elliptic PDEs
  • Finite element
  • L
  • Nonmatching grids
  • Schwarz alternating method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Maximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs. / Boulbrachene, Messaoud; Al Farei, Qais.

In: Applied Mathematics and Computation, Vol. 238, 01.07.2014, p. 21-29.

Research output: Contribution to journalArticle

@article{c5db6d6e48aa46ef96916e70a11b102b,
title = "Maximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs",
abstract = "In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of the geometrical convergence of both the continuous and corresponding discrete Schwarz sequences. We also give some numerical results to support the theory.",
keywords = "Elliptic PDEs, Finite element, L, Nonmatching grids, Schwarz alternating method",
author = "Messaoud Boulbrachene and {Al Farei}, Qais",
year = "2014",
month = "7",
day = "1",
doi = "10.1016/j.amc.2014.03.146",
language = "English",
volume = "238",
pages = "21--29",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Maximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs

AU - Boulbrachene, Messaoud

AU - Al Farei, Qais

PY - 2014/7/1

Y1 - 2014/7/1

N2 - In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of the geometrical convergence of both the continuous and corresponding discrete Schwarz sequences. We also give some numerical results to support the theory.

AB - In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of the geometrical convergence of both the continuous and corresponding discrete Schwarz sequences. We also give some numerical results to support the theory.

KW - Elliptic PDEs

KW - Finite element

KW - L

KW - Nonmatching grids

KW - Schwarz alternating method

UR - http://www.scopus.com/inward/record.url?scp=84899523411&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899523411&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2014.03.146

DO - 10.1016/j.amc.2014.03.146

M3 - Article

AN - SCOPUS:84899523411

VL - 238

SP - 21

EP - 29

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -