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Maximum norm analysis of an arbitrary number of nonmatching grids method for nonlinears elliptic PDEs. (English) Zbl 1397.65310

Summary: 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 \(L^\infty\) error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J60 Nonlinear elliptic equations
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