Higher-order finite element discretizations in a benchmark problem for incompressible flows

We present a numerical study of several finite element discretizations applied to a benchmark problem for the two-dimensional steady state incompressible Navier-Stokes equations defined in Schafer and Turek (The benchmark problem 'Flow around a cylinder. In Flow Simulation with High-Performance Computers II Notes on Numerical Fluid Mechanics, vol. 52, Hirschel EH (ed.). Vieweg: Wiesbaden, 1996; 547-566). The discretizations are compared with respect to the accuracy of the computed benchmark parameters. Higher-order isoparametric Finite element discretizations turned out to be by far the most accurate. The discrete systems obtained with higher-order discretizations are solved with a modified coupled multigrid method whose behaviour within the benchmark problem is also studied numerically. Copyright (C) 2001 John Wiley & Sons, Ltd.