On the convergence of generalized Schwarz algorithms for solving obstacle problems with elliptic operators

In this paper, multiplicative and additive generalized Schwarz algorithms for solving obstacle problems with elliptic operators are developed and analyzed. Compared with the classical Schwarz algorithms, in which the subproblems are coupled by the Dirichlet boundary conditions, the generalized Schwarz algorithms use Robin conditions with parameters as the transmission conditions on the interface boundaries. As a result, the convergence rate can be speeded up by choosing Robin parameters properly. Convergence of the algorithms is established. This work was supported by 973 national project of China (2004CB719402) and by national nature science foundation of China (10671060).