Preprint series: 03-41 , Preprints

MSC:

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

65N12 Stability and convergence of numerical methods

Abstract: We investigate a
nonconforming finite element on tensor product meshes applied to
convection-diffusion equations with dominating convection.\\
This (incomplete nonconforming $P_2$) element can be considered as an
enriched $Q_1^{rot}$ element (Rannacher-Turek element).
In difference to the $Q_1^{rot}$ element,
one obtains
a superclose property and superconvergence in the $H1$ seminorm.
Additionally, in the case of small diffusion parameters,
this enrichment of the $Q_1^{rot}$ element
leads to a stabilization in streamline direction similar to SDFEM.

Keywords: Nonconforming FEM, superconvergence, singularly perturbed problems, nonconforming bubbles

Upload: 2003-11-19-11-19