A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier-Stokes equations

作者：Xue, Jufeng; Shang, Yueqiang^*

来源：Journal of Applied Mathematics and Computing, 2018, 58(1-2): 95-110.

DOI：10.1007/s12190-017-1135-y

• Navier-Stokes equations
• Finite element
• Variational multiscale method
• Error estimate

In this report, we present and study a fully discrete finite element variational multiscale scheme for the unsteady incompressible Navier-Stokes equations where high Reynolds numbers are allowed. The scheme uses conforming finite element pairs for spatial discretization and a three-point difference formula for temporal discretization which is of second-order, where a stabilization term based on two local Gauss integrations is employed to stabilize the numerical scheme. We prove stability of the scheme, derive a priori error estimates for the fully discrete solution, and finally, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed numerical scheme.

• 出版日期2018-10
• 单位西南大学