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On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs. (English) Zbl 1010.65052
Proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems are given. The nonlinear partial differential equations (PDEs) are known to have solutions by the monotone method. In particular it is shown that an additive Schwarz method for some scalar equations as well as systems converges on finitely many subdomains even in case that multiple solutions are possible.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
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