Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method. (English) Zbl 1388.74091
Summary: 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 \(O(h^{1+\min\{\alpha,1\}})\) is established for both the displacement approximation in \(H^1\)-norm and the stress approximation in \(L^2\)-norm under a mesh assumption, where \(\alpha > 0\) 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74B05 | Classical linear elasticity |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
linear elasticity; hybrid stress finite element; superconvergence; recovery; a posteriori error estimatorReferences:
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