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

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  • Xu, Chao
  • Shi, Dongyang

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(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.

Suggested Citation

  • Xu, Chao & Shi, Dongyang, 2019. "Superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 1-11.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:1-11
    DOI: 10.1016/j.amc.2018.08.015
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    References listed on IDEAS

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    1. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 216-226.
    2. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 1-16.
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    Cited by:

    1. Shougui Zhang & Xiyong Cui & Guihua Xiong & Ruisheng Ran, 2024. "An Optimal ADMM for Unilateral Obstacle Problems," Mathematics, MDPI, vol. 12(12), pages 1-16, June.
    2. Dongyang Shi & Lifang Pei, 2020. "New High Accuracy Analysis of a Double Set Parameter Nonconforming Element for the Clamped Kirchhoff Plate Unilaterally Constrained by an Elastic Obstacle," Mathematics, MDPI, vol. 8(11), pages 1-13, November.

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