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

Abstract EN

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.