{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:56:44Z","timestamp":1776837404509,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"345","license":[{"start":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T00:00:00Z","timestamp":1719705600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We propose a new numerical 2-point flux for a quasilinear convection\u2013diffusion equation. This numerical flux is shown to be an approximation of the numerical flux derived from the solution of a two-point Dirichlet boundary value problem for the projection of the continuous flux onto the line connecting neighboring collocation points. The later approach generalizes an idea first proposed by Scharfetter and Gummel [IEEE Trans. Electron Devices\n                    <bold>16<\/bold>\n                    (1969), pp.\u00a064\u201377] for linear drift-diffusion equations. We establish first that the new flux satisfies sufficient properties ensuring the convergence of the associate finite volume scheme, while respecting the maximum principle. Then, we pay attention to the long time behavior of the scheme: we show relative entropy decay properties satisfied by the new numerical flux as well as by the generalized Scharfetter-Gummel flux. The proof of these properties uses a generalization of some discrete (and continuous) log-Sobolev inequalities. The corresponding decay of the relative entropy of the continuous solution is proved in the appendix. Some 1D numerical experiments confirm the theoretical results.\n                  <\/p>","DOI":"10.1090\/mcom\/3870","type":"journal-article","created":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T09:35:04Z","timestamp":1684920904000},"page":"203-231","source":"Crossref","is-referenced-by-count":2,"title":["A monotone numerical flux for quasilinear convection diffusion equation"],"prefix":"10.1090","volume":"93","author":[{"given":"C.","family":"Chainais-Hillairet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Eymard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Fuhrmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2023,6,30]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1007\/s00211-012-0448-x","article-title":"A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme","volume":"121","author":"Bessemoulin-Chatard, Marianne","year":"2012","journal-title":"Numer. 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