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

Messaoud Boulbrachene; Qais Al Farei

doi:10.1016/j.amc.2014.03.146

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

Messaoud Boulbrachene^*, Qais Al Farei

^*Corresponding author for this work

Mathematics

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

5 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 language	English
Pages (from-to)	21-29
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	238
DOIs	https://doi.org/10.1016/j.amc.2014.03.146
Publication status	Published - Jul 1 2014

Keywords

Elliptic PDEs
Finite element
L
Nonmatching grids
Schwarz alternating method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.03.146

Cite this

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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",

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AU - Boulbrachene, Messaoud

AU - Al Farei, Qais

PY - 2014/7/1

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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

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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