A parallel two-grid method based on finite element approximations for the 2D/3D Navier–Stokes equations with damping

Based on two-grid discretizations, this paper introduces a parallel finite element method for the 2D/3D Navier–Stokes equations with damping. In this method, we first solve a fully nonlinear problem on a global coarse grid, and then solve linearized residual subproblems in overlapping fine grid subdomains to update the coarse grid solution by some local and parallel procedures. With the help of local a priori estimate for the finite element solution, errors of the approximate solution from the proposed method are estimated. Performance of the proposed method is also illustrated by some numerical tests.