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Pointwise a Posteriori Error Analysis of a Finite Element Method for the Signorini Problem

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Abstract

In this article, we develop a posteriori error control of conforming finite element method in maximum norm for the one-body contact problem. The reliability and the efficiency of the error estimator is discussed. The upper and lower barriers of the exact solution \({\varvec{u}}\) have been constructed by rectifying the discrete solution \({\varvec{u}}_{{\varvec{h}}}\) properly and they are crucially used in obtaining the reliability estimates. Other key ingredients of the analysis are the sign property of the quasi-discrete contact force density as well as bounds on the Green’s matrix of the divergence type operator. Numerical experiments are presented for a two dimensional contact problems that exhibit reliability and efficiency of the error estimator confirming theoretical findings.

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Funding

RK work is supported by the Council for Scientific and Industrial Research (CSIR)

and KP work is supported by SERB MATRICS grant.

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

    Rohit Khandelwal & Kamana Porwal

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  1. Rohit Khandelwal
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  2. Kamana Porwal
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Correspondence to Kamana Porwal.

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Khandelwal, R., Porwal, K. Pointwise a Posteriori Error Analysis of a Finite Element Method for the Signorini Problem. J Sci Comput 91, 42 (2022). https://doi.org/10.1007/s10915-022-01811-0

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  • DOI: https://doi.org/10.1007/s10915-022-01811-0

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