Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method

Abstract

We consider two-level finite element discretization methods for the stream function formulation of the Navier--Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh and then solvinga linear system on the fine mesh. The basic result states that the errors between the coarse and fine meshes are related superlinearly. This paper demonstrates that the two-level method can be implemented to approximate efficiently solutions to the Navier--Stokes equations. Two fluid flow calculations are considered to test problems which have a known solution and the driven cavity problem. Stream function contours are displayed showing the main features of the flow.