{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T09:08:26Z","timestamp":1774688906099,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> Mimetic discretization methods for the numerical solution of continuum mechanics \n\t\t\tproblems directly use vector calculus and differential forms identities for their \n\t\t\tderivation and analysis. Fully mimetic discretizations satisfy discrete analogs of \n\t\t\tthe continuum theory results used to derive energy inequalities. Consequently, \n\t\t\tcontinuum arguments carry over and can be used to show that discrete problems \n\t\t\tare well-posed and discrete solutions converge. A fully mimetic discrete vector \n\t\t\tcalculus on three dimensional tensor product grids is derived and its key properties \n\t\t\tproven. Opinions regarding the future of the field are stated.<\/jats:p>","DOI":"10.2478\/cmam-2011-0002","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:18:45Z","timestamp":1366042725000},"page":"23-66","source":"Crossref","is-referenced-by-count":21,"title":["A Discrete Vector Calculus in Tensor Grids"],"prefix":"10.2478","volume":"11","author":[{"given":"Nicolas","family":"Robidoux","sequence":"first","affiliation":[{"name":"1Department of Mathematics and Computer Science, Laurentian University, Sudbury ON P3E 2C6, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stanly","family":"Steinberg","sequence":"additional","affiliation":[{"name":"2Department of Mathematics and Statistics, University of New Mexico, Albuquerque NM 87131-1141 USA."}],"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\/11\/1\/article-p23.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2011-0002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:47Z","timestamp":1619101307000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/1\/article-p23.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2011-0002","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2011]]}}}