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Adaptive Quadratic Finite Element Method for the Unilateral Contact Problem

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Abstract

In this paper, we present and analyze a posteriori error estimates in the energy norm of a quadratic finite element method for the frictionless unilateral contact problem. The reliability and the efficiency of a posteriori error estimator is discussed. The suitable decomposition of the discrete space \({\mathbf{V^h_0}}\) and a discrete space \({\mathbf{Q^h}}\), where the discrete counterpart of the contact force density is defined, play crucial role in deriving a posteriori error estimates. Numerical results are presented exhibiting the reliability and the efficiency of the proposed error estimator.

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Funding

The second author’s work is supported by CSIR Extramural Research Grant.

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Authors and Affiliations

  1. Department of Mathematics, Government Science College Chikhli, Navsari, Gujarat, 396521, India

    Rohit Khandelwal

  2. Department of Mathematics, Indian Institute of Technology, Delhi, 110016, India

    Kamana Porwal & Tanvi Wadhawan

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  1. Rohit Khandelwal
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  2. Kamana Porwal
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  3. Tanvi Wadhawan
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Correspondence to Kamana Porwal.

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Khandelwal, R., Porwal, K. & Wadhawan, T. Adaptive Quadratic Finite Element Method for the Unilateral Contact Problem. J Sci Comput 96, 20 (2023). https://doi.org/10.1007/s10915-023-02206-5

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