{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:09:52Z","timestamp":1760267392852},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We devise and analyze vertex-based, P\u00e9clet-robust, lowest-order schemes for advection-diffusion equations that support polyhedral meshes. The schemes are formulated using Compatible Discrete Operators (CDO), namely, primal and dual discrete differential operators, a discrete contraction operator for advection, and a discrete Hodge operator for diffusion. Moreover, discrete boundary operators are devised to weakly enforce Dirichlet boundary conditions. The analysis sheds new light on the theory of Friedrichs' operators at the purely algebraic level. Moreover, an extension of the stability analysis hinging on inf-sup conditions is presented to incorporate divergence-free velocity fields under some assumptions. Error bounds and convergence rates for smooth solutions are derived and numerical results are presented on three-dimensional polyhedral meshes.<\/jats:p>","DOI":"10.1515\/cmam-2016-0007","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T18:38:56Z","timestamp":1456511936000},"page":"187-212","source":"Crossref","is-referenced-by-count":6,"title":["Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations"],"prefix":"10.1515","volume":"16","author":[{"given":"Pierre","family":"Cantin","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Est, CERMICS (ENPC), 77455 Marne la Vall\u00e9e Cedex 2; and EDF R&D, 6 quai Watier, BP 49, 78401 Chatou, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandre","family":"Ern","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Est, CERMICS (ENPC), 77455 Marne la Vall\u00e9e Cedex 2, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,2,26]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/2\/article-p187.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0007\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0007\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:59:44Z","timestamp":1680303584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0007\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,26]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2,20]]},"published-print":{"date-parts":[[2016,4,1]]}},"alternative-id":["10.1515\/cmam-2016-0007"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2016-0007","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,26]]}}}