Two-level defect-correction stabilized finite element method for Navier–Stokes equations with friction boundary conditions

Abstract

In this paper, we consider a two-level defect-correction stabilized finite element method (DCS-FEM) for the incompressible Navier-Stokes equation with friction boundary conditions based on local Gauss integration. The main idea is to combine the two-level strategy with the defectcorrection method. Using this technique, the simplified two-level DCSFEM and the Newton two-level DCSFEM are proposed and some error estimates are derived. Finally, the numerical results are displayed to confirm our theoretical findings.

Low‐order stabilized finite element methods for the unsteady Stokes/Navier‐Stokes equations with friction boundary conditions

“…Kashiwabara studied discrete variational inequality problem for the Stokes equations with leak boundary conditions of friction type. Other theoretical and numerical results for the steady and unsteady Stokes/Navier‐Stokes problems with such boundary conditions can be found in previous studies …”

“…Other theoretical and numerical results for the steady and unsteady Stokes/Navier-Stokes problems with such boundary conditions can be found in previous studies. [15][16][17][18][19][20][21] The development of an efficient finite element method for the incompressible flow simulations is an important but challenging problem. The importance of ensuring the compatibility of the component approximations of velocity and pressure by satisfying the discrete inf-sup condition is widely known.…”

A penalty‐FEM for navier‐stokes type variational inequality with nonlinear damping term

“…Other numerical theory results about Navier-Stokes problems with friction type boundary conditions can be found in Refs. [8][9][10][11].…”

A Two‐Parameter Stabilized Finite Element Method for Incompressible Flows

“…In this paper, we consider a combined method which maintains the best algorithmic features of the above mentioned subgrid stabilized method and the two‐grid methods. We refer to Xu for the basic ideas of two‐grid methods, and, for example, to for two‐grid methods for the Navier–Stokes equations, among others. Specifically, we first solve a nonlinear Navier–Stokes problem on a coarse grid, and then solve a linear problem on a fine grid to correct the coarse grid solution.…”