{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:39:38Z","timestamp":1775882378031,"version":"3.50.1"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The solution operator in a Petrov Galerkin scheme in Hilbert spaces\nis an oblique projection with quasi-best approximation property. The latter\nestimate involves a multiplicative constant and the best-possible of those\nis the target of the note: We present a new direct proof of the formula of the\nquasi-best approximation constant and avoid the direct application of\nthe Kato lemma. In fact, our characterisation leads to another proof of\nthe Kato oblique projection lemma. The abstract result in Hilbert spaces\nis embedded in the setting of\nthe best-approximation of conforming Petrov Galerkin schemes with a rich\nhistory that eventually led to the Tantardini\u2013Veeser formula. A final\napplication discusses the classical nonconforming schemes with a smoother\nin this framework.<\/jats:p>","DOI":"10.1515\/cmam-2025-0025","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T18:09:22Z","timestamp":1748628562000},"page":"581-585","source":"Crossref","is-referenced-by-count":3,"title":["A Note on the Quasi-Best Approximation Constant"],"prefix":"10.1515","volume":"25","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[{"name":"Department of Mathematics , 98596 Humboldt-Universit\u00e4t zu Berlin , Berlin , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2025,5,29]]},"reference":[{"key":"2025070217063879053_j_cmam-2025-0025_ref_001","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, D.  Gallistl and M.  Schedensack,\nAdaptive nonconforming Crouzeix\u2013Raviart FEM for eigenvalue problems,\nMath. Comp. 84 (2015), no. 293, 1061\u20131087.","DOI":"10.1090\/S0025-5718-2014-02894-9"},{"key":"2025070217063879053_j_cmam-2025-0025_ref_002","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and N.  Nataraj,\nA priori and a posteriori error analysis of the Crouzeix\u2013Raviart and Morley FEM with original and modified right-hand sides,\nComput. Methods Appl. Math. 21 (2021), no. 2, 289\u2013315.","DOI":"10.1515\/cmam-2021-0029"},{"key":"2025070217063879053_j_cmam-2025-0025_ref_003","doi-asserted-by":"crossref","unstructured":"A.  Ern and J.-L.  Guermond,\nFinite Elements II\u2014Galerkin Approximation, Elliptic and Mixed PDEs,\nTexts Appl. Math. 73,\nSpringer, Cham, 2021.","DOI":"10.1007\/978-3-030-56923-5"},{"key":"2025070217063879053_j_cmam-2025-0025_ref_004","doi-asserted-by":"crossref","unstructured":"D. B.  Szyld,\nThe many proofs of an identity on the norm of oblique projections,\nNumer. Algorithms 42 (2006), no. 3\u20134, 309\u2013323.","DOI":"10.1007\/s11075-006-9046-2"},{"key":"2025070217063879053_j_cmam-2025-0025_ref_005","doi-asserted-by":"crossref","unstructured":"F.  Tantardini and A.  Veeser,\nThe \n                  \n                     \n                        \n                           L\n                           2\n                        \n                     \n                     \n                     L^{2}\n                  \n               -projection and quasi-optimality of Galerkin methods for parabolic equations,\nSIAM J. Numer. Anal. 54 (2016), no. 1, 317\u2013340.","DOI":"10.1137\/140996811"},{"key":"2025070217063879053_j_cmam-2025-0025_ref_006","doi-asserted-by":"crossref","unstructured":"A.  Veeser and P.  Zanotti,\nQuasi-optimal nonconforming methods for symmetric elliptic problems. I\u2014Abstract theory,\nSIAM J. Numer. Anal. 56 (2018), no. 3, 1621\u20131642.","DOI":"10.1137\/17M1116362"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0025\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0025\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T17:07:06Z","timestamp":1751476026000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0025\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,29]]},"references-count":6,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,6,17]]},"published-print":{"date-parts":[[2025,7,1]]}},"alternative-id":["10.1515\/cmam-2025-0025"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2025-0025","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,29]]}}}