A parallel Oseen-linearized algorithm for the stationary Navier–Stokes equations

Based on two-grid discretizations and domain decomposition, a parallel Oseen-linearized finite element algorithm for the stationary Navier–Stokes equations with moderate or large viscosity parameter is proposed and analyzed. The key idea of the algorithm is to first solve a nonlinear problem by Picard iterative method on a coarse grid, and then to solve an Oseen problem in parallel on a fine grid to correct the coarse grid solution. By using local a priori error estimate for the finite element solution and under the uniqueness condition, error bounds of the corresponding finite element solution are analyzed. Numerical results are also given to demonstrate the high efficiency of the algorithm.