A two-level finite element method with backtracking technique for the Navier-Stokes equations at high Reynolds numbers

Abstract

A two-level finite element method with backtracking technique for the stationaryNavier-Stokes equations at high Reynolds numbers is considered. The basic idea of the method is to first solve a fully nonlinearNavier-Stokes equations with a subgrid stabilization term on a coarse grid, and then solve a subgrid stabilized linear fine grid problem based on one step of Newton iteration,and finally, solve a linear correction problem on the coarse mesh. The theoretical and numerical results show that, with suitable scalings of algorithmic parameters,the method can yield an optimal convergence rate. Numerical results are also given to verify theoretical predictions and demonstrate the effectiveness of the method.