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Superconvergence of a nonconforming low order finite element

by Risch, U..

Series: 2003-41, Preprints

65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N12 Stability and convergence of numerical methods

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.

Nonconforming FEM, superconvergence,