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An analysis of finite volume element method for solving the Signorini problem

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  • Zhang, Tie
  • Li, Zheng

Abstract

We propose and analyze the finite volume element method for solving the Signorini problem. The stability and the optimal H1-convergence rate are given. Particularly, we establish a superclose interpolation estimate for the bilinear form of this method. Based on this estimate and the interpolation post-processing technique, we derive an O(h32)-order superconvergence in the H1-norm under a proper regularity condition. Finally, an asymptotically exact a posteriori error estimator also is given for the error ∥u−uh∥1.

Suggested Citation

  • Zhang, Tie & Li, Zheng, 2015. "An analysis of finite volume element method for solving the Signorini problem," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 830-841.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:830-841
    DOI: 10.1016/j.amc.2015.08.106
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    Cited by:

    1. Zhang, Shougui, 2018. "Two projection methods for the solution of Signorini problems," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 75-86.
    2. Li, Xiaolin & Dong, Haiyun, 2019. "Analysis of the element-free Galerkin method for Signorini problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 41-56.
    3. Yuping Zeng & Fen Liang, 2020. "Convergence Analysis of a Discontinuous Finite Volume Method for the Signorini Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-49, August.
    4. Jie Zhao & Hong Li & Zhichao Fang & Yang Liu, 2019. "A Mixed Finite Volume Element Method for Time-Fractional Reaction-Diffusion Equations on Triangular Grids," Mathematics, MDPI, vol. 7(7), pages 1-18, July.

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