A defect-correction stabilized finite element method for Navier-Stokes equations with friction boundary conditions

摘要

In this paper, we consider a defect-correction stabilized finite element method for incompressible Navier-Stokes equations with friction boundary conditions whose variational formulation is the variational inequality problem of the second kind with Navier-Stokes operator. In the defect step, an artificial viscosity parameter σ is added to the Reynolds number as a stability factor, and the Oseen iterative scheme is applied in the correction step. H~1 × L~2 error estimations are derived for the one-step defect-correction stabilized finite element method. In the end, some numerical results are presented to verify the theoretical analysis.