{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:17:08Z","timestamp":1760267828463,"version":"3.40.5"},"reference-count":31,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1190009","1210391"],"award-info":[{"award-number":["1190009","1210391"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study a fourth-order div problem and its approximation by the discontinuous Petrov\u2013Galerkin method with optimal test functions.\nWe present two variants, based on first and second-order systems.\nIn both cases, we prove well-posedness of the formulation and quasi-optimal convergence of the approximation.\nOur analysis includes the fully-discrete schemes with approximated test functions, for general dimension and polynomial degree in the first-order case, and for two dimensions and lowest-order approximation in the second-order case.\nNumerical results illustrate the performance for quasi-uniform and adaptively refined meshes.<\/jats:p>","DOI":"10.1515\/cmam-2021-0246","type":"journal-article","created":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T20:30:04Z","timestamp":1653337804000},"page":"545-562","source":"Crossref","is-referenced-by-count":1,"title":["DPG Methods for a Fourth-Order div Problem"],"prefix":"10.1515","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5034-6593","authenticated-orcid":false,"given":"Thomas","family":"F\u00fchrer","sequence":"first","affiliation":[{"name":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2142-2961","authenticated-orcid":false,"given":"Pablo","family":"Herrera","sequence":"additional","affiliation":[{"name":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5171-1457","authenticated-orcid":false,"given":"Norbert","family":"Heuer","sequence":"additional","affiliation":[{"name":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,5,24]]},"reference":[{"key":"2023033112440912547_j_cmam-2021-0246_ref_001","doi-asserted-by":"crossref","unstructured":"S. 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Demkowicz, T. F\u00fchrer, N. Heuer and X. Tian,\nThe double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babu\u0161ka and Brezzi),\nComput. Math. Appl. 95 (2021), 41\u201366.","DOI":"10.1016\/j.camwa.2020.10.002"},{"key":"2023033112440912547_j_cmam-2021-0246_ref_008","doi-asserted-by":"crossref","unstructured":"L. Demkowicz and J. Gopalakrishnan,\nA class of discontinuous Petrov\u2013Galerkin methods. II. Optimal test functions,\nNumer. Methods Partial Differential Equations 27 (2011), no. 1, 70\u2013105.","DOI":"10.1002\/num.20640"},{"key":"2023033112440912547_j_cmam-2021-0246_ref_009","doi-asserted-by":"crossref","unstructured":"L. Demkowicz, J. Gopalakrishnan and A. H. Niemi,\nA class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity,\nAppl. Numer. Math. 62 (2012), no. 4, 396\u2013427.","DOI":"10.1016\/j.apnum.2011.09.002"},{"key":"2023033112440912547_j_cmam-2021-0246_ref_010","doi-asserted-by":"crossref","unstructured":"L. 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Math. 132 (2016), no. 1, 185\u2013200.","DOI":"10.1007\/s00211-015-0708-7"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0246\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0246\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T17:00:26Z","timestamp":1680282026000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0246\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,24]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3,26]]},"published-print":{"date-parts":[[2022,7,1]]}},"alternative-id":["10.1515\/cmam-2021-0246"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2021-0246","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2022,5,24]]}}}