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

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara＇s 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O（h^1＋min{α,1}） is established for both the displacement approximation in H~1-norm and the stress approximation in L^2-norm under a mesh assumption, where α 〉 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.