A V-cycle Multigrid And Domain Decomposition Method For Mortar-type Rotated Q₁ Element

In this thesis, we mainly consider the following two problems.A V-cycle multigrid method is presented for the mortar-type rotated Q₁ nonconforming element in the first chapter. The uniform convergence rate is proven, which is independent of mesh size and mesh level. Numerical experiments are presented to confirm our theoretical results.In the second chapter, we present an additive Schwarz precondi-tioner for the rotated Q₁ finite element discretization of second order elliptic problem. Since there is no finite element subspace of rotated Q₁ finite element space, a special coarse space is used, we prove the condition number of preconditioned problem is optimal.