A two-level stabilized quadratic equal-order finite element variational multiscale method for incompressible flows

摘要

A two-level stabilized quadratic equal-order variational multiscale method based on the finite element discretization is proposed for numerically solving the steady incompressible Navier-Stokes equations at high Reynolds numbers. In this method, a stabilized solution is first obtained by solving a fully stabilized nonlinear system on a coarse grid, and then the solution is corrected by solving a stabilized linear problem on a fine grid. Under the condition of N∥f∥H−1(Ω)ν(ν+α)<1, the stability of the present method is analyzed, and error estimates of the approximate solutions from the proposed method are deduced. The effectiveness of the proposed method is demonstrated by some numerical results.