Local and parallel finite element algorithms based on domain decomposition for the 2D/3D Stokes equations with damping

Based on two-grid discretization and domain decomposition approach, this paper presents and studies two local and parallel finite element algorithms for the 2D/3D steady Stokes equations with nonlinear damping term. Starting point of the algorithms is that for a solution of the Stokes equations with damping, we first approximate the low-frequency component on a relatively coarse grid, and then compute the high-frequency component on a locally fine grid via some local and parallel procedures. The proposed algorithms are easy to implement and have low communication complexity. With the use of the technical tool of local a priori estimate for finite element solution, we derive error estimates of the approximate solutions from the proposed algorithms. Some numerical results are provided to test the validity of the present algorithms.