Abstract:

In the present work we consider aspects of the formulation and numerical implementation of the BDM-Element (Brezzi, Douglas, Marini [1985], Stenberg [1988]). This element is based on an extended dual Hellinger-Reissner principle which leads to optimal convergence rates for the stresses and displacements. The element is characterized by a non-symmetric approximation of the stress field (Fraeijs de Veubeke [1975]) which implies an approximation of the work-conjugate rotation field. Conditions for stability checks and optimal convergence of this element have been pointed out by Stein & Rolfes [1990]. Within this paper we discuss in detail algorithmic aspects of the implementation and perform comparisons with respect to the approximation behaviour of the Q1-, Pian-Sumihara- and the recently developed Q1/E5-Element.