01-06
On Higher Order Finite Element Discretizations for the Incompressible Navier-Stokes Equations in Three Dimensions
by John, V.; Matthies G.; Tobiska L.
Preprint series: 01-06, Preprints
The paper is published: Proceedings of ECCOMAS 2001, on CD-Rom, ISBN 0 905 091 12 4, 2001
- MSC:
- 65N22 Solution of discretized equations, See also {65Fxx, 65Hxx}
- 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
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