{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T17:30:01Z","timestamp":1784050201500,"version":"3.55.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,7,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe prove convergence and quasi-optimality of a lowest-order adaptive\nboundary element method for a weakly-singular integral equation in 2D.\nThe adaptive mesh-refinement is driven by the weighted-residual\nerror estimator. By proving that this estimator is not only reliable, but under some\nregularity assumptions on the given data also efficient on locally refined meshes, we characterize the approximation class in terms of the Galerkin error only.\nIn particular, this yields that no\nadaptive strategy can do better, and the weighted-residual error estimator is thus an optimal choice to steer the adaptive mesh-refinement. As a side result, we prove a\nweak form of the saturation assumption.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0010","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T16:01:19Z","timestamp":1380297679000},"page":"305-332","source":"Crossref","is-referenced-by-count":26,"title":["Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods"],"prefix":"10.1515","volume":"13","author":[{"given":"Markus","family":"Aurada","sequence":"first","affiliation":[{"name":"1Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr.\u00a08\u201310, 1040 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Feischl","sequence":"additional","affiliation":[{"name":"2Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr.\u00a08\u201310, 1040 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"F\u00fchrer","sequence":"additional","affiliation":[{"name":"3Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr.\u00a08\u201310, 1040 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Karkulik","sequence":"additional","affiliation":[{"name":"4Departamento de Matem\u00e1ticas, Avenida Vicu\u00f1a Mackenna 4860, Santiago, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dirk","family":"Praetorius","sequence":"additional","affiliation":[{"name":"5Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr.\u00a08\u201310, 1040 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/3\/article-p305.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/3\/article-p305.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:42Z","timestamp":1614481422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0010\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,1]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0010","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,1]]}}}