{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T07:21:28Z","timestamp":1720250488649},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"Abstract<\/jats:title>\n The paper proves the convergence of the finite volume approximate solution\nof a convection-diffusion equation with an \n \n \n \n L<\/m:mi>\n 1<\/m:mn>\n <\/m:msup>\n <\/m:math>\n ${L^{1}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> right-hand side to the unique renormalized solution. The main difficulties are to handle the noncoercive character of the operator and the \n \n \n \n L<\/m:mi>\n 1<\/m:mn>\n <\/m:msup>\n <\/m:math>\n ${L^{1}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> data. Mixing the techniques of renormalized solutions and the finite volume method allows one to derive estimates for the discrete solutions and in particular a discrete version of the decay of the truncated energy.\nIndeed, as in the continuous case, the decay of the truncated energy is crucial to show that the limit of the approximate solution is the renormalized solution.<\/jats:p>","DOI":"10.1515\/cmam-2016-0034","type":"journal-article","created":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T10:04:11Z","timestamp":1478685851000},"page":"85-104","source":"Crossref","is-referenced-by-count":2,"title":["Finite Volume Scheme and Renormalized Solutions for a Noncoercive Elliptic Problem with\nL<\/i>\n 1<\/sup> Data"],"prefix":"10.1515","volume":"17","author":[{"given":"Sarah","family":"Leclavier","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Rapha\u00ebl Salem, UMR 6085 CNRS-Universit\u00e9 de Rouen, Avenue de l\u2019universit\u00e9, BP 12, 76801 Saint Etienne du Rouvray, France"}]}],"member":"374","published-online":{"date-parts":[[2016,11,8]]},"reference":[{"key":"2023033115185155110_j_cmam-2016-0034_ref_001_w2aab3b7e3169b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Ben Cheick M. and Guib\u00e9 O.,\nR\u00e9sultats d\u2019existence et d\u2019unicit\u00e9 pour une classe de probl\u00e8mes non lin\u00e9aires et non coercifs,\nC.R. 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