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