{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:47:54Z","timestamp":1776728874276,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"244","license":[{"start":{"date-parts":[[2004,3,26]],"date-time":"2004-03-26T00:00:00Z","timestamp":1080259200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We present two approaches to the a\u00a0posteriori error analysis for prescribed mean curvature equations. The main difference between them concerns the estimation of the residual: without or with computable weights. In the second case, the weights are related to the eigenvalues of the underlying operator and thus provide local and computable information about the conditioning. We analyze the two approaches from a theoretical viewpoint. Moreover, we investigate and compare the performance of the derived indicators in an adaptive procedure. Our theoretical and practical results show that it is advantageous to estimate the residual in a weighted way.<\/p>","DOI":"10.1090\/s0025-5718-03-01507-2","type":"journal-article","created":{"date-parts":[[2003,6,20]],"date-time":"2003-06-20T10:23:27Z","timestamp":1056104607000},"page":"1611-1634","source":"Crossref","is-referenced-by-count":19,"title":["On the a posteriori error analysis for equations of prescribed mean curvature"],"prefix":"10.1090","volume":"72","author":[{"given":"Francesca","family":"Fierro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Veeser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2003,3,26]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[AO00] Mark Ainsworth and J. 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Nochetto, and Kunibert G. Siebert, Local problems on stars: a posteriori error estimators, convergence, and performance, Math. Comp., posted on November 7, 2002, PII S0025-5718(02)-01463-1 (to appear in print)."},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1137\/S0036142999360044","article-title":"Data oscillation and convergence of adaptive FEM","volume":"38","author":"Morin, Pedro","year":"2000","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"17","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1098\/rsta.1969.0033","article-title":"The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables","volume":"264","author":"Serrin, J.","year":"1969","journal-title":"Philos. Trans. Roy. Soc. London Ser. 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