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2013 Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES
Abida Harbi
J. Appl. Math. 2013: 1-21 (2013). DOI: 10.1155/2013/893182

Abstract

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 error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

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Abida Harbi. "Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES." J. Appl. Math. 2013 1 - 21, 2013. https://doi.org/10.1155/2013/893182

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950923
MathSciNet: MR3133964
Digital Object Identifier: 10.1155/2013/893182

Rights: Copyright © 2013 Hindawi

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