On Schwarz Alternating Methods for Nonlinear Elliptic PDEs

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers several Schwarz alternating methods for nonlinear elliptic problems. We show that Schwarz alternating methods can be embedded in the framework of common techniques such as Banach and Schauder fixed point methods and global inversion methods used to solve these nonlinear problems.