On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
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.
nonlinear partial differential equations
scientific article; zbMATH DE number 1837414