Multigrid methods for the generalized stokes equations based on mixed finite element methods

摘要

Multigrid method are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion. To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are con- Structed explicitly.