Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs

In this paper, we prove uniform convergence of the standard finite element method for a Schwarz alternating procedure for nonlinear elliptic partial differential equations in the context of linear subdomain problems and nonmatching grids. The method stands on the combination of the convergence of linear Schwarz sequences with standard finite element L-error estimate for linear problems