{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T08:31:24Z","timestamp":1771489884239,"version":"3.50.1"},"reference-count":45,"publisher":"Walter de Gruyter GmbH","issue":"0","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>An abstract property (<jats:bold>H<\/jats:bold>) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-order equivalent nonstandard finite element methods for biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates the impact of (<jats:bold>H<\/jats:bold>) to the a posteriori error analysis and establishes known and novel explicit residualbased a posteriori error estimates. The abstract framework applies to Morley, two versions of discontinuous Galerkin, <jats:italic>C<\/jats:italic>\n                  <jats:sup>0<\/jats:sup> interior penalty, as well as weakly overpenalized symmetric interior penalty schemes for the biharmonic equation with a general source term in <jats:italic>H<\/jats:italic>\n                  <jats:sup>\u22122<\/jats:sup>(\u03a9).<\/jats:p>","DOI":"10.1515\/jnma-2022-0092","type":"journal-article","created":{"date-parts":[[2023,1,31]],"date-time":"2023-01-31T16:03:41Z","timestamp":1675181021000},"source":"Crossref","is-referenced-by-count":2,"title":["Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation"],"prefix":"10.1515","volume":"0","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany"},{"name":"Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benedikt","family":"Gr\u00e4\u00dfle","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neela","family":"Nataraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,1,31]]},"reference":[{"key":"2023090112092836442_j_jnma-2022-0092_ref_001","doi-asserted-by":"crossref","unstructured":"G. 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