New convergence analysis for assumed stress hybrid quadrilateral finite element method
Binjie Li Xiaoping Xie Shiquan Zhang
Discrete & Continuous Dynamical Systems - B 2017, 22(7): 2831-2856 doi: 10.3934/dcdsb.2017153

New error estimates are established for Pian and Sumihara's (PS) 4-node assumed stress hybrid quadrilateral element [T.H.H. Pian, K. Sumihara, Rational approach for assumed stress finite elements, Int. J. Numer. Methods Engrg., 20 (1984), 1685-1695], which is widely used in engineering computation. Based on an equivalent displacement-based formulation to the PS element, we show that the numerical strain and a postprocessed numerical stress are uniformly convergent with respect to the Lamé constant $λ$ on the meshes produced through the uniform bisection procedure. Within this analysis framework, we also show that both the numerical strain and stress are uniformly convergent on meshes which are stable for the $Q_1-P_0$ Stokes element.

keywords: Assumed stress hybrid element linear elasticity quadrilateral mesh uniformly convergent

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