A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations I: Spatial Discretization (Journal of Computational Mathematics, 2004)
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
Keywords: Navier-Stokes equations; Mixed finite element; Error estimate; Finite element method.