## 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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