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Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations

by V. John.

Series: 2001-18, Preprints

65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N55 Multigrid methods; domain decomposition

This paper presents a numerical study of the 3D flow around a cylinder
which was defined as a benchmark problem for the steady state Navier--Stokes
equations within the DFG high priority research program
{\it Flow Simulation with High--Performance Computers} by Schäfer and Turek (1996).
The first part of the study is a comparison of several finite element discretizations
with respect to the accuracy of the computed benchmark parameters. It turns out that boundary
fitted higher order finite element methods are in general most accurate.
Our numerical study improves the hitherto existing reference values for the
benchmark parameters considerably. The second part of the study
deals with efficient and robust solvers for the discrete saddle point
problems. All considered solvers are based on coupled multigrid methods. The
flexible GMRES method with a multiple discretization multigrid methods proves
to be the best solver.

incompressible Navier-Stokes equations, higher order finite element methods, coupled multigrid methods, multiple discretization multigrid method, flexible GMRES