Parallel defect-correction algorithms based on finite element discretization for the Navier-Stokes equations

Based on a fully overlapping domain decomposition technique and finite element discretization, two parallel defect-correction algorithms for the stationary Navier-Stokes equations with high Reynolds numbers are proposed and investigated. In these algorithms, each processor first solves an artificial viscosity stabilized Navier-Stokes equations by Newton or Picard iterative method, and then diffuses the system in the correction steps where only a linear problem needs to be solved at each step. All the computations are performed in parallel on global composite meshes that are fine around a particular subdomain and coarse elsewhere. The algorithms have low communication complexity. They can yield an approximate solution with an accuracy comparable to that of the standard finite element solution. Numerical tests demonstrated the effectiveness of the algorithms.