97-35

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

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

 

Preprint series: 97-35, Preprints

The paper is published: Comput. Methods Appl. Mech. Engrg. 166(1998), 85-97

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

 

Abstract: 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.

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


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