Superconvergence of a nonconforming low order finite element

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 rot element (Rannacher–Turek element). In difference to this Q 1 rot 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 rot element leads to a stabilization in streamline direction similar to SDFEM.