Superconvergence of a nonconforming low order finite element

Authors:
Uwe Risch
Affiliations:
Institute for Analysis and Numerics, Otto von Guericke University, PF 4120, 39016 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 P"2) element can be considered as an enriched parametric Q"1^r^o^t element (Rannacher-Turek element). In difference to this Q"1^r^o^t element, one obtains a supercloseness property and superconvergence in the H^1 seminorm. Additionally, in the case of small diffusion parameters, the enrichment of the Q"1^r^o^t element leads to a stabilization in streamline direction similar to SDFEM.