On the stability of BDMS and PEERS elements

Authors:
Marco Lonsing;Rüdiger Verfürth
Affiliations:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany;Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany
Venue:
Numerische Mathematik
Year:
2004

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Abstract

Using “Fortin operators” we give a new proof of stability for Stenberg’s family of BDMS elements in linear elasticity. Our approach yields the inf-sup condition with respect to the standard norms, which is indispensable for a posteriori error analysis. Furthermore our technique allows the construction of another family of finite elements strongly related to the classical PEERS element. The given estimates are robust for nearly incompressible materials.