Maximum norm analysis of an arbitrary number of nonmatching grids method for nonlinears elliptic PDEs
type: Item
instance of: scholarly article
title: Maximum norm analysis of an arbitrary number of nonmatching grids method for nonlinears elliptic PDEs
zbMATH Open document ID: 1397.65310
DOI: 10.1155/2013/893182
author: A. Harbi
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on an arbitrary number of overlapping subdomains with nonmatching grids. We consider a domain which is the union of an arbitrary number \(m\) of overlapping subdomains where each subdomain has its own independently generated grid. The \(m\) meshes being mutually independent on the overlap regions, a triangle belonging to one triangulation does not necessarily belong to the other ones. Under the a Lipschitz assumption 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: 65N55
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6950923
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/893182
OpenAlex ID: W2054354879
Wikidata QID: Q59005062
description: scientific article; zbMATH DE number 6950923