On monotone iteration and Schwarz methods for nonlinear parabolic PDEs.
The author proves convergence of two Schwarz methods for a class of scalar nonlinear parabolic partial differential equations (PDEs). The quasi-monotone nonincreasing case of a coupled system of PDEs is studied and proof of convergence of an additive Schwarz method on finitely many subdomains is given. The other cases (quasi-monotone nondecreasing and mixed quasi-monotone) are also discussed.
scientific article; zbMATH DE number 2032606
scientific article