Maximum norm analysis of a nonmatching grids method for nonlinear elliptic PDES

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. © copyright 2011 a. harbi and m. boulbrachene.