{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:00:36Z","timestamp":1757311236220},"reference-count":40,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes.\nAn assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential.\nThis property is fundamental to handle the stability issues related to the Joule heating term.\nThen the convergence to a weak solution is established.\nFinally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.<\/jats:p>","DOI":"10.1515\/cmam-2019-0144","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T10:49:34Z","timestamp":1595414974000},"page":"69-87","source":"Crossref","is-referenced-by-count":5,"title":["Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model"],"prefix":"10.1515","volume":"21","author":[{"given":"Mustapha","family":"Ghilani","sequence":"first","affiliation":[{"name":"Moulay Isma\u00efl University , ENSAM-Mekn\u00e8s, B.P. 15290 EL Mansour 50 500 Mekn\u00e8s , Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"El Houssaine","family":"Quenjel","sequence":"additional","affiliation":[{"name":"C\u00f4te d\u2019Azur University , LJAD, CNRS UMR 7351, and COFFEE team, INRIA Sophia Antipolis M\u00e9editerran\u00e9e, Parc Valrose 06108 Nice Cedex 02 , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Rhoudaf","sequence":"additional","affiliation":[{"name":"Moulay Isma\u00efl University , Faculty of Sciences, B.P. 11201 Zitoune 50 500 Mekn\u00e8s , Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,7,16]]},"reference":[{"key":"2023033111222073365_j_cmam-2019-0144_ref_001","doi-asserted-by":"crossref","unstructured":"M.  Afif and B.  Amaziane,\nConvergence of finite volume schemes for a degenerate convection\u2013diffusion equation arising in flow in porous media,\nComput. Methods Appl. Mech. Engrg. 191 (2002), no. 46, 5265\u20135286.","DOI":"10.1016\/S0045-7825(02)00458-9"},{"key":"2023033111222073365_j_cmam-2019-0144_ref_002","doi-asserted-by":"crossref","unstructured":"G.  Akrivis and S.  Larsson,\nLinearly implicit finite element methods for the time-dependent Joule heating problem,\nBIT 45 (2005), no. 3, 429\u2013442.","DOI":"10.1007\/s10543-005-0008-1"},{"key":"2023033111222073365_j_cmam-2019-0144_ref_003","unstructured":"W.  Allegretto, Y.  Liu and A.  Zhou,\nA box scheme for coupled systems resulting from microsensor thermistor problems,\nDyn. Contin. Discrete Impuls. Syst. 5 (1999), no. 1\u20134, 209\u2013223."},{"key":"2023033111222073365_j_cmam-2019-0144_ref_004","doi-asserted-by":"crossref","unstructured":"W.  Allegretto and H.  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