A parallel finite element discretization algorithm based on grad-div stabilization for the Navier-Stokes equations (Q6540640)

The authors numerically solve a Dirichlet boundary value problem in a bounded domain by using a system composed of steady incompressible Navier-Stokes equations and the incompressibility equation. They use a parallel grad-div stabilized FEM based on an entire overlapping domain decomposition. Some new global a priori error estimates for the grad-div stabilized FEM are introduced along with some local a priori estimate for the FEM solution of a grad-div stabilized and linearized Navier-Stokes equations. Some numerical experiments concerning four benchmark problems are carried out. From these experiments as well as from their global a priori error estimates, the authors conclude that the introduced method is more accurate in terms of speed than the parallel FEM algorithm without grad-div stabilization and, on the othr hand, consumes much less computation time than the standard FEM with grad-div stabilization.