{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T18:19:41Z","timestamp":1780424381240,"version":"3.54.1"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CA 151\/22-2"],"award-info":[{"award-number":["CA 151\/22-2"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016838","name":"Berlin Mathematical School","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100016838","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2023,4,30]]},"DOI":"10.1137\/21m139921x","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T09:24:21Z","timestamp":1682328261000},"page":"812-836","source":"Crossref","is-referenced-by-count":17,"title":["Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian"],"prefix":"10.1137","volume":"61","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Berlin, 10099, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sophie","family":"Puttkammer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Berlin, 10099, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-007-0066-1"},{"key":"ref3","first-page":"751","volume":"22","author":"Bebendorf M.","year":"2003","journal-title":"J. Math. Anal. Appl."},{"key":"ref4","first-page":"641","volume-title":"Handbook of Numerical Analysis","author":"Babu\u0161ka I.","year":"1991"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000012"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34797-9"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"ref8","first-page":"1","volume-title":"Encyclopedia of Computational Mechanics","author":"Carstensen C.","year":"2018","edition":"2"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100378"},{"key":"x10","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-018-0984-0"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2013.12.003"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-013-0559-z"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2014-02833-0"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2014.07.019"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.4208\/jcm.1108-m3677"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/130915856"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2014-02894-9"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2017-0044"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396415"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2021-0029"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.4208\/jcm.1908-m2018-0174"},{"key":"ref23","first-page":"33","volume":"7","author":"Crouzeix M.","year":"1973","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/16M1068050"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/18M1212276"},{"key":"ref26","first-page":"131","volume-title":"Geometric Modeling","author":"de Boor C.","year":"1987"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/0733054"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/dru054"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-014-0671-8"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-014-9821-5"},{"key":"x31","first-page":"260","volume":"15","author":"Hong Q.","year":"2018","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.03.048"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-012-4382-2"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.02.020"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s13160-019-00351-9"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144502409093"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1017\/S0001925900004546"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0662-x"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971163"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/BF00252910"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396493"},{"key":"ref42","volume-title":"An Analysis of the Finite Element Method","author":"Strang G.","year":"2008","edition":"2"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-008-9018-y"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1137\/13091467X"},{"key":"ref45","series-title":"Monogr. Res. Notes Math.","volume-title":"Finite Element Methods for Eigenvalue Problems","author":"Sun J.","year":"2017"},{"key":"ref46","series-title":"Lecture Notes of the Unione Matematica Italiana 3","volume-title":"An Introduction to Sobolev Spaces and Interpolation Spaces","author":"Tartar L.","year":"2007"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199679423.001.0001"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/17M1151651"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/BF01890556"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.06.004"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-011-9185-4"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T20:11:22Z","timestamp":1682712682000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M139921X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,24]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4,30]]}},"alternative-id":["10.1137\/21M139921X"],"URL":"https:\/\/doi.org\/10.1137\/21m139921x","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,24]]}}}