Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES

A. Harbi and M. Boulbrachene

Journal of Applied Mathematics, 2011, vol. 2011, issue 1

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.

Date: 2011
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https://doi.org/10.1155/2011/605140

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2011:y:2011:i:1:n:605140

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