{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T14:24:06Z","timestamp":1726410246017},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540709404"},{"type":"electronic","value":"9783540709428"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-70942-8_1","type":"book-chapter","created":{"date-parts":[[2007,5,13]],"date-time":"2007-05-13T13:19:32Z","timestamp":1179062372000},"page":"1-15","source":"Crossref","is-referenced-by-count":0,"title":["On the Discretization of the Coupled Heat and Electrical Diffusion Problems"],"prefix":"10.1007","author":[{"given":"Abdallah","family":"Bradji","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rapha\u00e8le","family":"Herbin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"1_CR1","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: A hybrid finite volume schemes for the discretization of anistropic diffusion operator on general meshes (submitted)"},{"key":"1_CR2","series-title":"Lecture Notes Ser. Comput.","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1142\/9789814355858_0002","volume-title":"Computing in Euclidean geometry","author":"M. Bern","year":"1992","unstructured":"Bern, M., Eppstein, D.: Mesh generation and optimal triangulation. In: Computing in Euclidean geometry. Lecture Notes Ser. Comput., vol.\u00a01, pp. 23\u201390. World Sci. Publ., River Edge (1992)"},{"issue":"2","key":"1_CR3","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1006\/jdeq.1993.1092","volume":"105","author":"L. Boccardo","year":"1993","unstructured":"Boccardo, L., Gallou\u00ebt, T., Vazquez, J.-L.: Nonlinear Elliptic Equations in R n without Growth Restrictions on the Data. Journal of Differential Equations\u00a0105(2), 334\u2013363 (1993)","journal-title":"Journal of Differential Equations"},{"key":"1_CR4","first-page":"241","volume":"22","author":"P. B\u00e9nilan","year":"1995","unstructured":"B\u00e9nilan, P., Boccardo, L., Gallou\u00ebt, T., Gariepy, R., Pierre, M., Vazquez, J.-L.: An L 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola. Norm. Sup. Pisa\u00a022, 241\u2013273 (1995)","journal-title":"Ann. Scuola. Norm. Sup. Pisa"},{"key":"1_CR5","unstructured":"Bradji, A., Herbin, R.: Discretization of ohmic losses by the finite element and the finite volume method (in preparation)"},{"key":"1_CR6","unstructured":"Casado-Diaz, J., Chacon Rebollo, T., Girault, V., Gomez, M., Murat, F.: Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L 1 (submitted)"},{"key":"1_CR7","first-page":"17","volume-title":"Handbook of Numerical Analysis, vol.\u00a0II","author":"P.A. Ciarlet","year":"1991","unstructured":"Ciarlet, P.A.: Basic error estimates for elliptic problems. In: Handbook of Numerical Analysis, vol.\u00a0II, pp. 17\u2013352. North-Holland, Amsterdam (1991)"},{"issue":"5","key":"1_CR8","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1142\/S0218202596000298","volume":"6","author":"S. Clain","year":"1996","unstructured":"Clain, S.: Finite element approximations for Laplace operator with right hand side measure. Math. Models Meth. App. Sci. 6 n\u00b0 5 (1996) 713\u2013719","journal-title":"Math. Models Meth. App. Sci."},{"issue":"4","key":"1_CR9","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1051\/m2an:2001135","volume":"35","author":"Y. Coudi\u00e8re","year":"2001","unstructured":"Coudi\u00e8re, Y., Gallou\u00ebt, T., Herbin, R.: Discrete Sobolev inequalities and L p error estimates for approximate finite volume solutions of convection diffusion equations. M2AN\u00a035(4), 767\u2013778 (2001)","journal-title":"M2AN"},{"key":"1_CR10","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/BF01758989","volume":"170","author":"A. Dall\u2019aglio","year":"1996","unstructured":"Dall\u2019aglio, A.: Approximated solutions of equations with L 1 solutions wiht L 1 data. Application to the H\u2013convergence of quasi\u2013linear parabolic equations. Ann. Mat. Pura Appl.\u00a0170, 207\u2013240 (1996)","journal-title":"Ann. Mat. Pura Appl."},{"issue":"6","key":"1_CR11","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1137\/S0036142902405205","volume":"41","author":"J. Droniou","year":"2003","unstructured":"Droniou, J., Gallou\u00ebt, T., Herbin, R.: A finite volumes schemes for a noncoercive elliptic equation with measure data. SIAM J. Numer. Anal. 41 n\u00b0 6 (2003) 1997-2031","journal-title":"SIAM J. Numer. Anal."},{"key":"1_CR12","doi-asserted-by":"crossref","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: Finite volume methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. II, pp. 723\u20131020 (2000)","DOI":"10.1016\/S1570-8659(00)07005-8"},{"key":"1_CR13","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s002110050412","volume":"82","author":"R. Eymard","year":"1999","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: Convergence of finite volume schemes for semilinear convection diffusion equations. Numer. Math.\u00a082, 91\u2013116 (1999)","journal-title":"Numer. Math."},{"key":"1_CR14","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1137\/S0036142901397083","volume":"41","author":"R. Eymard","year":"2003","unstructured":"Eymard, R., Gallou\u00ebt, T.: H-convergence and numerical schemes for elliptic problems. SIAM J. Numer. Anal.\u00a041, 539\u2013562 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1093\/imanum\/dri036","volume":"26","author":"R. Eymard","year":"2006","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: A cell-centered finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension. IMA J. of Numer. Anal.\u00a026, 326\u2013353 (2006)","journal-title":"IMA J. of Numer. Anal."},{"key":"1_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/0378-7753(95)02269-4","volume":"58","author":"J.R. Ferguson","year":"1996","unstructured":"Ferguson, J.R., Fiard, J.M., Herbin, R.: A mathematical model of solid oxide fuel cells. Journal of Power Sources\u00a058, 109\u2013122 (1996)","journal-title":"Journal of Power Sources"},{"key":"1_CR17","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0045-7825(94)90065-5","volume":"115","author":"J.M. Fiard","year":"1994","unstructured":"Fiard, J.M., Herbin, R.: Comparison between finite volume and finite element methods for an elliptic system arising in electrochemical engineerings. Comput. Methods App. Mech. Engrg.\u00a0115, 315\u2013338 (1994)","journal-title":"Comput. Methods App. Mech. Engrg."},{"key":"1_CR18","first-page":"81","volume":"338","author":"T. Gallou\u00ebt","year":"2004","unstructured":"Gallou\u00ebt, T., Herbin, R.: Convergence of linear finite element for diffusion equations with measure data. CRAS\u00a0338, 81\u201384 (2004)","journal-title":"CRAS"},{"key":"1_CR19","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0893-9659(94)90030-2","volume":"7","author":"T. Gallou\u00ebt","year":"1994","unstructured":"Gallou\u00ebt, T., Herbin, R.: Existence of a solution to a coupled elliptic system. Appl. Math. Lett.\u00a07, 49\u201355 (1994)","journal-title":"Appl. Math. Lett."},{"key":"1_CR20","first-page":"155","volume-title":"Finite Volumes for Complex Applications, II","author":"T. Gallou\u00ebt","year":"1999","unstructured":"Gallou\u00ebt, T., Herbin, R.: Finite volume approximation of elliptic problems with irregular data. In: Benkhaldoun, F., H\u00e4nel, M., Vilsmeier, R. (eds.) Finite Volumes for Complex Applications, II, pp. 155\u2013162. Hermes, Paris (1999)"},{"key":"1_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-7643-7384-9_1","volume":"63","author":"T. Gallou\u00ebt","year":"2005","unstructured":"Gallou\u00ebt, T.: Measure data and numerical schemes for elliptic problems. Progress in Nonlinear Differential Equations and their Applications\u00a063, 1\u201313 (2005)","journal-title":"Progress in Nonlinear Differential Equations and their Applications"},{"key":"1_CR22","doi-asserted-by":"crossref","unstructured":"Murat, F.: Equations elliptiques non lin\u00e9aires avec second membre L 1 ou mesure. In: Actes du 26-\u00e8me Congr\u00e8s d\u2019Analyse Num\u00e9rique, Les Karellis, Universit\u00e9 de Lyon (1994)","DOI":"10.5802\/jedp.538"},{"key":"1_CR23","doi-asserted-by":"crossref","first-page":"189","DOI":"10.5802\/aif.204","volume":"15","author":"G. Stampacchia","year":"1965","unstructured":"Stampacchia, G.: Le probl\u00e8me de Dirichlet pour les \u00e9quations elliptiques du second orders \u00e0 coefficients discontinus. Ann. Inst. Fourier\u00a015, 189\u2013258 (1965)","journal-title":"Ann. Inst. Fourier"},{"key":"1_CR24","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/BF01436386","volume":"21","author":"R. Scott","year":"1973","unstructured":"Scott, R.: Finite element convergence for singular data. Numer. Math.\u00a021, 317\u2013327 (1973)","journal-title":"Numer. Math."}],"container-title":["Lecture Notes in Computer Science","Numerical Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-70942-8_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T00:13:02Z","timestamp":1605744782000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-70942-8_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540709404","9783540709428"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-70942-8_1","relation":{},"subject":[]}}