求解混合有限元离散二阶椭圆问题的并行Robin-Robin迭代方法

he Robin-Robin iterative method is a kind of nonoverlapping domain decomposition method, in which the information is exchanged by the Robin boundary condition on the interface. The purpose of this paper is to introduce a parallel Robin-Robin iterative method for the mixed finite element approximation of the second order elliptic problems, and give a condition for choosing Robin parameters and relaxation parameter. Based on the spectral theory of the block operator matrices and eigenvalue estimates of the Neumann to Dirichlet operator for the mixed finite element methods, it is proved that the convergence rate of the algorithm is independent of the mesh size and the jump in the coefficient. Some numerical experiments are presented to confirm our results.