03-41
Superconvergence of a nonconforming low order finite element
by Risch, U.
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
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