Maximum norm analysis of a nonmatching grids method for nonlinear elliptic PDEs
type: Item
instance of: scholarly article
title: Maximum norm analysis of a nonmatching grids method for nonlinear elliptic PDEs
zbMATH Open document ID: 1235.65134
DOI: 10.1155/2011/605140
published in: Journal of Applied Mathematics
publication date: 2012-04-04T00:00:00Z
review text: Summary: We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal \(L^\infty\) error estimate between the discrete Schwarz sequence and the exact solution of the PDE.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J99
zbMATH DE Number: 6021608
Wikidata QID: Q58690466
author: A. Harbi
author: M. Boulbrachene
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/605140
OpenAlex ID: W2165877445
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description: scientific article; zbMATH DE number 6021608