RESUMEN
In this paper, we present
two stable rectangular nonconforming mixed finite element methods for the
equations of linear elasticity in two space dimensions which produce direct approximations for the stress and displacement. In the first method, the
normal stress space of the matrixvalued stress space is taken
as the second order rotated Brezzi–Douglas–Fortin–Marini
element space [F. Brezzi and M. Fortin,
Mixed and Hybrid
Finite Element Methods, Springer-Verlag, New York, 1991], the enriched nonconforming
rotated Q1 element [Q. Lin,
L. Tobiska, and A. H. Zhou, IMA J. Numer. Anal., 25 (2005), pp. 160–181] is
taken for the shear stress, and the lowest
order Raviart–Thomas element space [P. A. Raviart and J. M. Thomas, in Mathematical Aspects of
the Finite Element Method, Lecture
Notes in Math. 606, Springer-Verlag, New York,
1977, pp. 292–315] is employed
to approximate the vector displacement field. The second
method is obtained from the
first one through dropping the interior degrees of the normal stress on each element.
A first order convergence rate is obtained for
both the stress and the displacement
for these methods based on
the superconvergence of the enriched
nonconforming rotated Q1 element.