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Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES

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  • Abida Harbi

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 of overlapping subdomains where each subdomain has its own independently generated grid. The 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 error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

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  • Abida Harbi, 2013. "Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-21, November.
    • Handle: RePEc:hin:jnljam:893182
    DOI: 10.1155/2013/893182
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