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

Based on a fully overlapping domain decomposition approach and a recent variational multiscale method, a parallel finite element variational multiscale method for the NavierStokes 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 H-1-norm of velocity and L-2-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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

A parallel finite element variational multiscale method for the NavierStokes equations with nonlinear slip boundary conditions is proposed and analyzed. Error estimates in H-1-norm of velocity and L-2-norm of pressure are derived using a technical tool of local a priori estimate for the finite element solution. Numerical results verify the validity of the theoretical predictions and show the high efficiency of the proposed method.