Summary: A NEW MIXED FORMULATION FOR ELASTICITY
Douglas N. Arnold Richard S. Falk
Department of Mathematics Department of Mathematics
University of Maryland Rutgers University
College Park, MD 20742 New Brunswick, NJ 08903
Dedicated to Professor Ivo Babuska on the occasion of his sixtieth birthday.
We propose a new mixed variational formulation for the equations of linear elasticity. It
does not require symmetric tensors and consequently is easy to discretize by adapting mixed
finite elements developed for scalar second order elliptic equations.
1980 Mathematics Subject Classification: Primary: 65N30; Secondary: 73 C35, 73K25
The first author was supported by NSF Grant DMS-8313247 and the second author by
NSF Grant DMS-8402616.
In this paper we present a new mixed variational formulation for the problem of
linear elastostatics. Our formulation is very similar to the classical Hellinger-Reissner
formulation, but appears superior for finite element discretization. To make plain the
relation between the Hellinger-Reissner formulation and the present one, we consider first
an elastic body occupying a region in Euclidean n-space (n = 2 or 3) subject to given