 
Summary: RECTANGULAR MIXED FINITE ELEMENTS FOR ELASTICITY
DOUGLAS N. ARNOLD AND GERARD AWANOU
Abstract. We present a family of stable rectangular mixed finite elements for plane elas
ticity. Each member of the family consists of a space of piecewise polynomials discretizing
the space of symmetric tensors in which the stress field is sought, and another to discretize
the space of vector fields in which the displacement is sought. These may be viewed as
analogues in the case of rectangular meshes of mixed finite elements recently proposed for
triangular meshes. As for the triangular case the elements are closely related to a discrete
version of the elasticity differential complex.
1. Introduction
Let be a simply connected polygonal domain of R2
, occupied by a linearly elastic body
which is clamped on and let H(div, , S) be the space of squareintegrable fields taking
values in S, the space of symmetric tensors, and which have square integrable divergence.
We denote as usual by L2
(, R2
) the space of square integrable vector fields with values in
R2
and Hk
(R, X) the space of functions with domain R R2
