Maximum norm analysis of a nonmatching grids method for nonlinear elliptic PDES

A. Harbi, M. Boulbrachene

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Abstract

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

Original languageEnglish
Article number605140
JournalJournal of Applied Mathematics
Volume2011
DOIs
Publication statusPublished - 2011

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ASJC Scopus subject areas

  • Applied Mathematics

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