Two‐grid stabilized algorithms for the steady Navier–Stokes equations with damping.

This paper presents and studies three two‐grid stabilized quadratic equal‐order finite element algorithms based on two local Gauss integrations for the steady Navier–Stokes equations with damping. In these algorithms, we first solve a stabilized nonlinear problem on a coarse grid, and then pass the coarse grid solution to a fine grid and solve a stabilized linear problem. Using some nonlinear analysis techniques, we analyze stability of the algorithms and derive optimal order error estimates of the approximate solutions. Theoretical and numerical results show that, when the algorithmic parameters are chosen appropriately, the accuracy of the approximate solutions computed by our two‐grid stabilized algorithms is comparable to that of solving a fully stabilized nonlinear problem on the same fine grid; however, our two‐grid algorithms save a large amount of CPU time than the one‐grid stabilized algorithm. [ABSTRACT FROM AUTHOR]