Mixed mortar element method for \(P^{NC}_1/P_0\) element and its multigrid method for the incompressible Stokes problem (Q1955436)

Summary: We discuss a mortar-type \(P^{NC}_1/P_0\) element method for the incompressible Stokes problem. We prove the inf-sup condition and obtain the optimal error estimate. Meanwhile, we propose a \(\mathcal W\)-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.