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2001-06

On Higher Order Finite Element Discretizations for the Incompressible Navier-Stokes Equations in Three Dimensions

by John, V., Matthies G., Tobiska L..


Series: 2001-06, Preprints

MSC:
65N22 Solution of discretized equations
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

Abstract:
For solving complex three-dimensional flow problems, many different approaches
have been developed. It turns out that both the discretization concept and the
solver designed for the discrete problem influences essentially the accuracy
and efficiency of the method. The main objective of the paper is to compare
lower and higher order finite element discretizations for the accurate and fast
solution of the incompressible Navier-Stokes equation in three space dimensions.
To this end, a well-defined benchmark problem of a channel flow around an
obstacle is used to quantify the gain in accuracy when higher order
discretizations are used. The comparison covers also the robust and
efficient solution of the discretized algebraic equations.

Keywords:
Navier-Stokes equations, higher order finite elements, multigrid solvers

This paper was published in:
Proceedings of ECCOMAS 2001, on CD-Rom, ISBN 0 905 091 12 4, 2001