{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:06Z","timestamp":1787333226342,"version":"build-2736575974"},"reference-count":45,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this paper, we consider a posteriori error estimators for obstacle problems. The variational inequality is reformulated as a mixed problem in terms of a discrete nodewise defined but variationally consistent Lagrange multiplier. Locally defined equilibrated fluxes and an $H(\\mathrm{div})$-conforming lifting define our estimator. To obtain a better local upper bound for the estimator, we introduce a different elementwise defined Lagrange multiplier. Although the upper and lower bounds are established for affine obstacles, we present generalizations to nonsmooth obstacles and to nonmatching meshes. Different numerical examples show the efficiency and reliability of our estimator. Due to its flexible construction principle and abstract framework, it can be also applied as an error indicator to more complex obstacle problems such as, e.g., American option pricing in financial mathematics.<\/jats:p>","DOI":"10.1137\/090773921","type":"journal-article","created":{"date-parts":[[2010,8,31]],"date-time":"2010-08-31T18:25:08Z","timestamp":1283279108000},"page":"2627-2658","source":"Crossref","is-referenced-by-count":22,"title":["A Posteriori Error Estimator for Obstacle Problems"],"prefix":"10.1137","volume":"32","author":[{"given":"Alexander","family":"Weiss","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Barbara I.","family":"Wohlmuth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Y. Achdou and O. 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Vohralik,\n                      A posteriori error estimation based on potential and flux reconstruction for the heat equation\n                      , SIAM J. Num. Anal. 48 (2010), pp. 198\u2013223.","DOI":"10.1137\/090759008"},{"key":"R26","first-page":"1","volume":"13","author":"Hager C.","year":"2010","journal-title":"J. Comput. Fin."},{"key":"R27","unstructured":"W. Han,\n                      A Posteriori Error Analysis via Duality Theory. 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Veeser,\n                      On a posteriori error estimation for constant obstacle problems\n                      , in Numerical Methods for Viscosity Solutions and Applications, Ser. Adv. Math. Appl. Sci. 59, M. Falcone and C. Makridakis, eds., World Scientific, Singapore, 2001, pp. 221\u2013234.","DOI":"10.1142\/9789812799807_0012"},{"key":"R42","unstructured":"R. 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