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

Abstract

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.