{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T21:33:44Z","timestamp":1779226424261,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe present a detailed survey of\ndiscrete functional analysis tools (consistency results, Poincar\u00e9 and Sobolev embedding inequalities, discrete <jats:italic>W<jats:sup>1,<jats:italic>p<\/jats:italic><\/jats:sup><\/jats:italic> compactness,\ndiscrete compactness in space and in time) for the so-called\nDiscrete Duality Finite Volume (DDFV) schemes\nin three space dimensions.\nWe concentrate mainly on the 3D CeVe-DDFV scheme presented\nin [IMA J. Numer. Anal., 32 (2012), pp.\u00a01574\u20131603].\nSome of our results are new, such as a general time-compactness result based upon the idea\nof Kruzhkov (1969); others generalize the ideas known for the 2D DDFV schemes or for traditional two-point-flux finite volume schemes.\nWe illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray\u2013Lions kind, and provide numerical results for this example.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0011","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T02:31:54Z","timestamp":1380594714000},"page":"369-410","source":"Crossref","is-referenced-by-count":15,"title":["On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems"],"prefix":"10.1515","volume":"13","author":[{"given":"Boris","family":"Andreianov","sequence":"first","affiliation":[{"name":"1Laboratoire de Math\u00e9matiques de Besan\u00e7on CNRS UMR 6623, Universit\u00e9 de Franche-Comt\u00e9, 16 route de Gray, 25030 Besan\u00e7on, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Bendahmane","sequence":"additional","affiliation":[{"name":"2Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 Victor Segalen, 33076 Bordeaux Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florence","family":"Hubert","sequence":"additional","affiliation":[{"name":"3LATP, Universit\u00e9 de Provence, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/4\/article-p369.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/4\/article-p369.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:42Z","timestamp":1614481422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0011\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,1]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0011","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,1]]}}}