Superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle

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Abstract Superconvergence analysis of nonconforming finite element methods (FEMs) are discussed for solving the second order variational inequality problem with displacement obstacle. The elements employed have a common typical character, i.e., the consistency error can reach order O ( h 3 / 2 − ɛ ) , nearly 1/2 order higher than their interpolation error when the exact solution of the considered problem belongs to H 5 / 2 − ɛ ( Ω ) for any e > 0. By making full use of special properties of the element’s interpolations and Bramble–Hilbert lemma, the superconvergence error estimates of order O ( h 3 / 2 − ɛ ) in the broken H1-norm are derived. Finally, some numerical results are provided to confirm the theoretical results.