A postprocessing mixed finite element method for the Navier-Stokes equations

A fully discrete postprocessing mixed finite element scheme is considered for solving the time-dependent Navier-Stokes equations. In the PP method, we only consider a non-linear equation in the coarse-level subspace and a linear problem in the fine-level subspace. The analysis shows that the PP scheme can reach the same accuracy as the standard Galerkin method with a very fine mesh size h by an appropriate choice of H. Numerical examples are provided that confirm both the theoretical analysis and the corresponding improvement in computational efficiency.