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

摘要

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(h3/2−ɛ), nearly 1/2 order higher than their interpolation error when the exact solution of the considered problem belongs to H5/2−ɛ(Ω) for any ε > 0. By making full use of special properties of the element’s interpolations and Bramble–Hilbert lemma, the superconvergence error estimates of order O(h3/2−ɛ) in the broken H1-norm are derived. Finally, some numerical results are provided to confirm the theoretical results.