On the nonlinear domain decomposition method
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Any domain decomposition or additive Schwarz method can be put into the abstract framework of subspace iteration. We consider generalizations of this method to the nonlinear case. The analysis shows under relatively weak assumptions that the nonlinear iteration converges locally with the same asymptotic speed as the corresponding linear iteration applied to the linearized problem.
AMS subject classification65H10 65N55
Key wordsDomain decomposition nonlinear problems preconditioner nonlinear elliptic problems
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