Maximum norm analysis of an arbitrary number of nonmatching grids method for nonlinears elliptic PDES

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. © 2013 abida harbi.