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

Abida Harbi | Zendy; Messaoud Boulbrachene | Zendy

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

Author(s) -

Abida Harbi,

Messaoud Boulbrachene

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/605140

Subject(s) - nonlinear system , norm (philosophy) , mathematics , finite element method , polygon mesh , algorithm , computer science , geometry , physics , quantum mechanics , political science , law , thermodynamics

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

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