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Summary: TWO REMARKS ON RECTANGULAR MIXED FINITE
ELEMENTS FOR ELASTICITY
GERARD AWANOU
Abstract. The lowest order nonconforming rectangular element in three dimen-
sions involves 54 degrees of freedom for the stress and 12 degrees of freedom for
the displacement. With a modest increase in the number of degrees of freedom (24
for the stress), we obtain a conforming rectangular element for linear elasticity in
three dimensions. Moreover, unlike the conforming plane rectangular or simplicial
elements, this element does not involve any vertex degrees of freedom. Second, we
remark that further low order elements can be constructed by approximating the
displacement with rigid body motions. This results in a pair of conforming ele-
ments with 72 degrees of freedom for the stress and 6 degrees of freedom for the
displacement.
1. Introduction
Let R3
be a contractible polygonal domain occupied by a linearly elastic body
and let L2
(, R3
) be the space of square integrable vector fields. We denote by S
the space of 3 × 3 symmetric matrix fields and by H(div, , S) the space of square
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