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Pointwise adaptive non-conforming finite element method for the obstacle problem

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Abstract

In this article, we develop a posteriori error analysis of a non-conforming finite element method in the supremum norm for the elliptic obstacle problem. In the analysis, the proper construction of the discrete Lagrange multiplier helps in obtaining the desired sign property of its average over the elements. The sub- and super-solutions, Green’s function, residual functional, and averaging operator are used crucially in proving the reliability of the proposed error estimator. Numerical results validating the theoretical results and illustrating the reliability and the efficiency of the error estimator are presented.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Kamana Porwal & Ritesh Singla

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  1. Kamana Porwal
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  2. Ritesh Singla
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Correspondence to Kamana Porwal.

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Communicated by Frederic Valentin.

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K. Porwal work is supported by DST-SERB MATRICS grant, India. R. Singla work is supported by institute fellowship by IIT Delhi, India.

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Porwal, K., Singla, R. Pointwise adaptive non-conforming finite element method for the obstacle problem. Comp. Appl. Math. 43, 150 (2024). https://doi.org/10.1007/s40314-024-02641-6

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