Convergence and superconvergence analysis of a nonconforming finite element method for solving the Signorini problem

Abstract In this paper, we present the Carey nonconforming finite element approximation of the variational inequality resulting from the Signorini problem. Firstly, we show that if the displacement field is of H 2 -regularity, the optimal convergence rate of  O ( h ) can be obtained with respect to the energy norm. Secondly, if stronger but reasonable  H 5 2 -regularity is available, the superconvergence rate of  O ( h 3 2 ) can be derived through the interpolated postprocessing technique. Finally, numerical experiments are given which are consistent with our theoretical analysis.

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