Mixed Mortar Element Method for P_1~(NC)/P_0 Element and Its Multigrid Method for the Incompressible Stokes Problem

摘要

We discuss a mortar-type P_1~(NC)/P_0 element method for the incompressible Stokes problem. We prove the inf-sup condition and obtain the optimal error estimate. Meanwhile, we propose a ω-cycle multigrid for solving this discrete problem and prove the optimal convergence of the multigrid method, that is, the convergence rate is independent of the mesh size and mesh level. Finally, numerical experiments are presented to confirm our theoretical results.