Multigrid method and multilevel additive preconditioner for mixed element method for non-self-adjoint and indefinite problems

摘要

In this paper, a V-cycle multigrid method is proposed for mixed element method for non-self-adjoint and indefinite second-order elliptic problems and the uniform convergence of the V-cycle multigrid method is proven under minimal regularity assumption. Meanwhile, a multilevel additive preconditioner is given for these problems and an optimal convergence rate for preconditioned GMRES method is obtained under minimal regularity assumption.