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

Abstract

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 Lamé 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.

References in corpus (1)

• A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids