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A Streamline-Diffusion Method for Nonconforming Finite Element Approxiamtions Applied to Convection-Diffusion Problems

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

Series: 1997-35, Preprints

65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds

We consider a nonconforming streamline-diffusion finite
element method for solving convection-diffusion problems.
The theoretical and numerical investigation for triangular
and tetrahedral meshes recently given by John, Maubach and
Tobiska has shown that the usual application of the SDFEM
gives not a sufficient stabilization. Additional parameter
dependent jump terms have been proposed which preserve the
same order of convergence as in the conforming case. The
error analysis has been essentially based on the existence
of a conforming finite element subspace of the
nonconforming space. Thus, the analysis can be applied for
example to the Crouzeix/Raviart element but not to the
nonconforming quadrilateral elements proposed by Rannacher
and Turek. In this paper, parameter free new jump terms are
developed which allow to handle both the triangular and the
quadrilateral case. Numerical experiments support the
theoretical predictions.

Convection-diffusion equations, streamline-diffusion finite element methods, n onconforming finite element methods, error estimates

This paper was published in:
Comput. Methods Appl. Mech. Engrg. 166(1998), 85-97