Superconvergence of a nonconforming low order finite element

Authors:
Uwe Risch
Affiliations:
Institute for Analysis and Numerics, Otto von Guericke University, PF, Magdeburg, Germany
Venue:
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Year:
2005

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Abstract

We investigate a nonconforming finite element on tensor product grids applied to diffusion-convection-reaction equations with dominating convection.This (incomplete nonconforming P2) element can be considered as an enriched parametric Q1rot element (Rannacher-Turek element). In difference to this Q1rot element, one obtains a supercloseness property and superconvergence in the H1 seminorm. Additionally, in the case of small diffusion parameters, the enrichment of the Q1rot element leads to a stabilization in streamline direction similar to SDFEM.