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

**Series:** 1997-35, Preprints

- 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

**This paper was published in:**

Comput. Methods Appl. Mech. Engrg. 166(1998), 85-97