A BDDC algorithm for the Stokes problem with weak Galerkin discretizations

The BDDC (balancing domain decomposition by constraints) methods have been applied successfully to solve the large sparse linear algebraic systems arising from conforming finite element discretizations of second order elliptic and Stokes problems. In this paper, the Stokes equations are discretized using the weak Galerkin method, a newly developed nonconforming finite element method. A BDDC algorithm is designed to solve the linear system such obtained. Edge/face velocity interface average and mean subdomain pressure are selected for the coarse problem. The condition number bounds of the BDDC preconditioned operator are analyzed, and the same rate of convergence is obtained as for conforming finite element methods. Numerical experiments are conducted to verify the theoretical results.