Local and parallel finite element algorithms for the incompressible Navier-Stokes equations with damping

Abstract

<p style='text-indent:20px;'>Using two-grid discretizations strategy, we present some local and parallel finite element algorithms for simulating the steady incompressible Navier-Stokes equations with a nonlinear damping term. In these algorithms, we compute a solution of the Navier-Stokes system with a nonlinear damping term on a coarse grid, and then adjust the solution by some local and parallel procedures on overlapped fine grid subomains. With the use of theoretical tool of local a priori estimate of the finite element solution, we estimate the error bounds of the approximate solutions, and derive the algorithmic parameter scalings. Finally, we give some numerical results to verify the theoretical predictions and demonstrate the efficiency of the proposed algorithms.</p>