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arXiv · 1502.01099

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

Yanhong Bai·Yongke Wu·Xiaoping Xie
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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 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.

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Yanhong Bai, Yongke Wu, Xiaoping Xie. 2015-02-04. Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method. https://doi.org/10.1007/s11425-016-5144-3

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