{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:54:09Z","timestamp":1766138049913,"version":"3.40.5"},"reference-count":38,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this article, we derive a reliable and efficient a posteriori error estimator in the supremum norm for a class of discontinuous Galerkin (DG) methods for the frictionless unilateral contact problem between two elastic bodies.\nThe proposed error estimator generalizes the basic residual type estimators for the linear problems in linear elasticity taking into account the nonlinearity on a part of the boundary.\nThe analysis hinges on the super- and sub-solutions constructed by modifying the discrete solution appropriately, and it is carried out in a unified manner which holds for several DG methods.\nThe terms arising from the contact stresses in the error estimator vanish on the discrete full contact set.\nWe illustrate the performance of the proposed error estimator via several numerical experiments in two dimensions.<\/jats:p>","DOI":"10.1515\/cmam-2021-0194","type":"journal-article","created":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T20:36:31Z","timestamp":1660250191000},"page":"189-217","source":"Crossref","is-referenced-by-count":1,"title":["Pointwise A Posteriori Error Control of Discontinuous Galerkin Methods for Unilateral Contact Problems"],"prefix":"10.1515","volume":"23","author":[{"given":"Rohit","family":"Khandelwal","sequence":"first","affiliation":[{"name":"Department of Mathematics , Indian Institute of Technology Delhi , New Delhi 110016 , India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5713-9498","authenticated-orcid":false,"given":"Kamana","family":"Porwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Indian Institute of Technology Delhi , New Delhi 110016 , India"}]}],"member":"374","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"2023033112515644060_j_cmam-2021-0194_ref_001","unstructured":"M. Ainsworth and J. T. Oden,\nA Posteriori Error Estimation in Finite Element Analysis,\nJohn Wiley & Sons, New York, 2011."},{"key":"2023033112515644060_j_cmam-2021-0194_ref_002","unstructured":"L. Ambrosio,\nLecture notes on elliptic partial differential equations,\nunpublished lecture notes, Scuola Normale Superiore di Pisa, 2015."},{"key":"2023033112515644060_j_cmam-2021-0194_ref_003","doi-asserted-by":"crossref","unstructured":"C. Baiocchi,\nEstimations d\u2019erreur dans \n                  \n                     \n                        \n                           L\n                           \u221e\n                        \n                     \n                     \n                     L^{\\infty}\n                  \n                pour les in\u00e9quations \u00e0 obstacle,\nMathematical Aspects of Finite Element Methods (Rome 1975),\nLecture Notes in Math. 606,\nSpringer, Berlin (1977), 27\u201334.","DOI":"10.1007\/BFb0064453"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_004","doi-asserted-by":"crossref","unstructured":"F. Ben Belgacem,\nNumerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element methods,\nSIAM J. Numer. Anal. 37 (2000), no. 4, 1198\u20131216.","DOI":"10.1137\/S0036142998347966"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_005","doi-asserted-by":"crossref","unstructured":"S. C. Brenner and L. R. Scott,\nThe Mathematical Theory of Finite Element Methods,\nTexts Appl. Math. 15,\nSpringer, New York, 2007.","DOI":"10.1007\/978-0-387-75934-0"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_006","doi-asserted-by":"crossref","unstructured":"F. Brezzi, W. W. Hager and P.-A. Raviart,\nError estimates for the finite element solution of variational inequalities,\nNumer. Math. 28 (1977), no. 4, 431\u2013443.","DOI":"10.1007\/BF01404345"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_007","doi-asserted-by":"crossref","unstructured":"R. Bustinza and F.-J. Sayas,\nError estimates for an LDG method applied to Signorini type problems,\nJ. Sci. Comput. 52 (2012), no. 2, 322\u2013339.","DOI":"10.1007\/s10915-011-9548-5"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_008","doi-asserted-by":"crossref","unstructured":"L. A. Caffarelli,\nFurther regularity for the Signorini problem,\nComm. Partial Differential Equations 4 (1979), no. 9, 1067\u20131075.","DOI":"10.1080\/03605307908820119"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_009","doi-asserted-by":"crossref","unstructured":"P. G. Ciarlet,\nThe Finite Element Method for Elliptic Problems,\nClassics Appl. Math. 40,\nSociety for Industrial and Applied Mathematics, Philadelphia, 2002.","DOI":"10.1137\/1.9780898719208"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_010","doi-asserted-by":"crossref","unstructured":"A. Demlow and E. H. Georgoulis,\nPointwise a posteriori error control for discontinuous Galerkin methods for elliptic problems,\nSIAM J. Numer. Anal. 50 (2012), no. 5, 2159\u20132181.","DOI":"10.1137\/110846397"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_011","doi-asserted-by":"crossref","unstructured":"G. Dolzmann and S. 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Wang, W. Han and X. Cheng,\nDiscontinuous Galerkin methods for solving the Signorini problem,\nIMA J. Numer. Anal. 31 (2011), no. 4, 1754\u20131772.","DOI":"10.1093\/imanum\/drr010"},{"key":"2023033112515644060_j_cmam-2021-0194_ref_038","doi-asserted-by":"crossref","unstructured":"A. Weiss and B. I. Wohlmuth,\nA posteriori error estimator and error control for contact problems,\nMath. 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