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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 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.

Suggested Citation

  • Abida Harbi, 2013. "Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:893182
    DOI: 10.1155/2013/893182
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    References listed on IDEAS

    as
    1. C. V. Pao, 1992. "Nonlinear Parabolic and Elliptic Equations," Springer Books, Springer, number 978-1-4615-3034-3, March.
    2. A. Harbi & M. Boulbrachene, 2011. "Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-18, November.
    3. A. Harbi & M. Boulbrachene, 2011. "Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
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