A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS Ⅰ: SPATIAL DISCRETIZATION

摘要

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a H~1-optimal velocity approximation and a L~2-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, one linear Stokes problem on the fine mesh with mesh size h H. The algorithm we study produces an approximate solution with the optimal, asymptotic in h, accuracy.