### 1999-28

by Knobloch, P., Tobiska, L..

**Series:** 1999-28, 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 loss of the Galerkin orthogonality

of the streamline diffusion method when applied to nonconforming finite

element approximations results in an additional error term which

cannot be estimated uniformly with respect to the perturbation parameter

for the standard piecewise linear or rotated bilinear elements. Therefore, we

construct a modified nonconforming

first order finite element space on shape regular triangular meshes satisfying

the patch test of order two and being related to the Crouzeix/Raviart

element. A rigorous error analysis of this

$P_1^{\mbox{\scriptsize\it mod}}$ element applied

to a streamline diffusion discretization is given. The numerical tests

show the robustness of the new method and the improved algebraic

properties of the discrete problem.

**Keywords:**