A parallel finite element variational multiscale method for the Navier-Stokes equations with nonlinear slip boundary conditions

Abstract

Based on a fully overlapping domain decomposition approach and a recent variational multiscale method, a parallel finite element variational multiscale method for the Navier-Stokes equations with nonlinear slip boundary conditions is proposed and analyzed. In this parallel method, a global composite grid is used to find a stabilized finite element solution for each subproblem, where a stabilization term based on two local Gauss integrations at the element level is employed to stabilize the system. Using the technical tool of local a priori estimate for the finite element solution, error estimates in H1-norm of velocity and L2-norm of pressure are derived. Numerical results are given to verify the validity of the theoretical predictions and illustrate the high efficiency of the proposed method.