A novel parallel two-step algorithm based on finite element discretization for the incompressible flow problem

Based on a two-step finite element method and fully overlapping domain decomposition technique, a parallel two-step algorithm for the incompressible flow problem is introduced and analyzed. In the new algorithm, all of the computations are performed in parallel on global composite meshes which are fine around the subdomain that we concentrate on but coarse elsewhere. Each processor first solves an original problem based on the P-1-P-1 stabilized finite element method and then solves a generalized Stokes problem based on the P-2-P-2 stabilized finite element method on a global composite mesh. The proposed algorithm is easy to implement. What's more, the new algorithm can yield more accurate solutions compared with the numerical solution obtained by the common two-step method. Numerical tests are presented to verify the efficiency and validity of the proposed algorithm.