Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM

Abstract In the third part of our investigations on averaging techniques for a posteriori error control in elasticity we focus on nonconforming finite elements in two dimensions. Kouhia and Stenberg [Comput. Methods Appl. Mech. Engrg. 124 (1995) 195] established robust a priori error estimates for a Galerkin-discretisation where the first component of the discrete displacement function is discretised with conforming and the second with nonconforming P1 finite elements. Here we study robust, i.e., λ-independent reliability and efficiency estimates for averaging error estimators. Numerical evidence supports that the reliability depends on the smoothness of given right-hand sides and independent of the structure of a shape-regular mesh.

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