A local and parallel Uzawa finite element method for the generalized Navier–Stokes equations

摘要

In this paper, we propose and develop a local and parallel Uzawa finite element method for the generalized Navier–Stokes equations. The Uzawa finite element method is no need to deal with the saddle point problem, and only solves one vector-valued elliptic equation and one simple scalar-valued equation. It has the geometric convergence with a crispation number γ what has nothing to do with the mesh size h. As for the local and parallel Uzawa finite element method, each subproblem is a global problem, but most of degrees of freedom originate from the subdomain. Moreover, the presented method is easy to be applied with less communication requirements and has good parallelism. Finally, numerical results verify the performance of the proposed method.