Parallel iterative finite element algorithms based on full domain partition for the stationary Navier–Stokes equations

Abstract

Based on full domain partition, three parallel iterative finite element algorithms for the stationary Navier–Stokes equations are proposed and analyzed. In these algorithms, each subproblem is defined in the entire domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Under some (strong) uniqueness conditions, errors of the parallel iterative finite element solutions are estimated. Some numerical results are also given which demonstrate the efficiency of the parallel iterative algorithms.