Parallel iterative stabilized finite element algorithms based on the lowest equal-order elements for the stationary Navier-Stokes equations

Based on a fully overlapping domain decomposition technique and the lowest equal-order finite elements, three parallel iterative stabilized finite element algorithms for the stationary Navier-Stokes equations are proposed and studied, where the stabilization term is based on two local Gauss integrations at element level. In these parallel algorithms, each processor independently computes a local stabilized solution in its own subdomain, making the algorithms have low communication cost and easy to implement based on a sequential solver. The algorithms can yield an approximate solution with an accuracy comparable to that of the standard stabilized finite element solution with a substantial reduction in computational time. Theoretical and numerical results demonstrated the effectiveness and efficiency of the algorithms. (c) 2019 Elsevier Inc. All rights reserved.