  We present stable mixed finite elements for planar linear elasticity on
general quadrilateral meshes. The symmetry of the stress tensor is imposed
weakly and so there are three primary variables, the stress tensor, the
displacement vector field, and the scalar rotation. We develop and analyze a
stable family of methods, indexed by an integer $r \geq 2$ and with rate of
convergence in the $L^2$ norm of order $r$ for all the variables. The methods
use Raviart-Thomas elements for the stress, piecewise tensor product
polynomials for the displacement, and piecewise polynomials for the rotation.
We also present a simple first order element, not belonging to this family. It
uses the lowest order BDM elements for the stress, and piecewise constants for
the displacement and rotation, and achieves first order convergence for all
three variables.

Numerical Analysis