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On Schwarz alternating methods for nonlinear elliptic PDEs. (English) Zbl 0959.65140
The author considers several Schwarz alternating method for solving nonlinear elliptic problems. It is shown that these methods with two overlapping subdomains can be embedded in the framework of Banach and Schauder fixed point methods or the theory of global inversion. Some versions of these methods are based on the parallel solution of linear problems in each subdomain.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65Y05 Parallel numerical computation
65H10 Numerical computation of solutions to systems of equations
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