  Superconvergence and a posteriori error estimators of recovery type are
analyzed for the 4-node hybrid stress quadrilateral finite element method
proposed by Pian and Sumihara (Int. J. Numer. Meth. Engrg., 1984, 20:
1685-1695) for linear elasticity problems. Uniform superconvergence of order
$O(h^{1+\min\{\alpha,1\}})$ with respect to the Lam\'{e} constant $\lambda$ is
established for both the recovered gradients of the displacement vector and the
stress tensor under a mesh assumption, where $\alpha>0$ is a parameter
characterizing the distortion of meshes from parallelograms to quadrilaterals.
A posteriori error estimators based on the recovered quantities are shown to be
asymptotically exact. Numerical experiments confirm the theoretical results.
