A nonconforming rotated Q1 approximation on tetrahedra

In this paper we construct an approximation that uses midpoints of edges on tetrahedra in three dimensions. The construction is based on the three-dimensional version of the rotated Q1-approximation proposed by Rannacher and Turek (1992) [6]. We prove a priori error estimates for finite element solutions of the elasticity equations using the new element. Since it contains (rotated) bilinear terms it performs substantially better than the standard constant strain element in bending. It also allows for under-integration (in the form of one point Gauss integration of volumetric terms) in near incompressible situations. Numerical examples are included.