{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:55Z","timestamp":1787336995559,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>Multilevel methods are applied to compute local and global Sobolev norms arising in adaptive boundary element methods. Combining this approach with an approximate computation of an error function we construct efficient and reliable a posteriori error estimators for arbitrary boundary element solutions related to either a Dirichlet or Neumann boundary value problem.<\/jats:p>","DOI":"10.1137\/s1064827599352999","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"604-616","source":"Crossref","is-referenced-by-count":11,"title":["Adaptive Boundary Element Methods Based on Computational Schemes for Sobolev Norms"],"prefix":"10.1137","volume":"22","author":[{"given":"O.","family":"Steinbach","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Randolph Bank, Hierarchical bases and the finite element method, Acta Numer., Vol. 5, Cambridge Univ. Press, Cambridge, 1996, 1\u20134399f:65161","DOI":"10.1017\/S0962492900002610"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-01106-0"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1990-1023042-6"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142993253503"},{"key":"R5","first-page":"521","volume":"48","author":"Crouzeix M.","year":"1987","journal-title":"Math. Comp."},{"key":"R6","unstructured":"R. Dautray and J.\u2010L. Lions,\n                      Mathematical Analysis and Numerical Methods for Science and Technology\n                      .\n                      Volume 4: Integral Equations and Numerical Methods\n                      , Springer, Berlin, 1990."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050331"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/20.2.203"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596311797"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(77)90186-X"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00081-9"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997316499"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684335"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"P. Oswald,\n                      Multilevel Finite Element Approximation\n                      , Teubner\u2013Verlag, Stuttgart, 1994.","DOI":"10.1007\/978-3-322-91215-2"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684352"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970968"},{"key":"R17","volume-title":"\u00dcber lokale und globale Fehlerabsch\u00e4tzungen f\u00fcr adaptive Randelementmethoden","author":"Schulz Heiko","year":"1997"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s100920070009"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"H. Schulz and O. Steinbach,\n                      A new a posteriori error estimator in adaptive direct boundary element methods\n                      ,\n                      the Neumann problem\n                      , in Multifield Problems. State of the Art, A. M. Sandig, W. Schiehlen, and W. L. Wendland, eds., Springer, Berlin, 2000, pp. 201\u2013208.","DOI":"10.1007\/978-3-662-04015-7_22"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1080\/00036819608840418"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397551"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388699"},{"key":"R23","unstructured":"Jinchao Xu, An introduction to multilevel methods, Numer. Math. Sci. Comput., Oxford Univ. Press, New York, 1997, 213\u201330299d:65329"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599352999","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:39:57Z","timestamp":1787333997000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599352999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599352999"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599352999","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}