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Superconvergence and a posteriori error estimators of recovery type areanalyzed for the 4-node hybrid stress quadrilateral finite element methodproposed 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 $\lambda$ isestablished for both the recovered gradients of the displacement vector and thestress tensor under a mesh assumption, where $\alpha>0$ is a parametercharacterizing the distortion of meshes from parallelograms to quadrilaterals.A posteriori error estimators based on the recovered quantities are shown to beasymptotically exact. Numerical experiments confirm the theoretical results.

Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method