{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T13:55:08Z","timestamp":1784555708922,"version":"3.55.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We develop an arbitrary-order primal method for diffusion problems on general polyhedral meshes.\nThe degrees of freedom are scalar-valued polynomials of the same order at mesh elements and faces.\nThe cornerstone of the method is a local (elementwise) discrete gradient reconstruction operator.\nThe design of the method additionally hinges on a least-squares penalty term on faces weakly enforcing the matching between local element- and face-based degrees of freedom.\nThe scheme is proved to optimally converge in the energy norm and in the <jats:italic>L<jats:sup>2<\/jats:sup>\n                  <\/jats:italic>-norm of the potential for smooth solutions.\nIn the lowest-order case, equivalence with the Hybrid Finite Volume method is shown.\nThe theoretical results are confirmed by numerical experiments up to order 4 on several polygonal meshes.<\/jats:p>","DOI":"10.1515\/cmam-2014-0018","type":"journal-article","created":{"date-parts":[[2014,6,17]],"date-time":"2014-06-17T14:29:23Z","timestamp":1403015363000},"page":"461-472","source":"Crossref","is-referenced-by-count":225,"title":["An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators"],"prefix":"10.1515","volume":"14","author":[{"given":"Daniele A.","family":"Di Pietro","sequence":"first","affiliation":[{"name":"University Montpellier 2, I3M, 34057 Montpellier Cedex 5, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Ern","sequence":"additional","affiliation":[{"name":"University Paris-Est, CERMICS (ENPC), 6\u20138 avenue Blaise Pascal, 77455 Marne-la-Vall\u00e9e Cedex 2, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon","family":"Lemaire","sequence":"additional","affiliation":[{"name":"University Paris-Est, CERMICS (ENPC), 6\u20138 avenue Blaise Pascal, 77455 Marne-la-Vall\u00e9e Cedex 2, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,6,17]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/4\/article-p461.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0018\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:02:38Z","timestamp":1680296558000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0018\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,8,20]]},"published-print":{"date-parts":[[2014,10,1]]}},"alternative-id":["10.1515\/cmam-2014-0018"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2014-0018","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,17]]}}}