{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:41:40Z","timestamp":1776724900394,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"228","license":[{"start":{"date-parts":[[2000,3,1]],"date-time":"2000-03-01T00:00:00Z","timestamp":951868800000},"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>We consider a variational problem which is equivalent to the electromagnetism system with absorbing conditions on a part of the boundary, and we prove that it is well-posed. Next we propose a discretization relying on a finite difference scheme for the time variable and on spectral elements for the space variables, and we derive error estimates between the exact and discrete solutions. R\u00e9sum\u00e9. On consid\u00e8re un probl\u00e8me variationnel \u00e9quivalent aux \u00e9quations de l\u2019\u00e9lectromagn\u00e9tisme avec conditions aux limites absorbantes sur une partie de la fronti\u00e8re, qu\u2019on prouve \u00eatre bien pos\u00e9. Puis on propose une discr\u00e9tisation de ce probl\u00e8me par sch\u00e9ma aux diff\u00e9rences finies en temps et \u00e9l\u00e9ments spectraux en espace, et on \u00e9tablit des estimations d\u2019erreur entre solutions exacte et approch\u00e9e.<\/p>","DOI":"10.1090\/s0025-5718-99-01086-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1497-1520","source":"Crossref","is-referenced-by-count":29,"title":["Spectral element discretization of the Maxwell equations"],"prefix":"10.1090","volume":"68","author":[{"given":"F.","family":"Belgacem","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Bernardi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[1999,3,1]]},"reference":[{"key":"1","unstructured":"[AB] A. Abdennadher, F. Ben Belgacem \u2014 Polynomial approximation of the eigenvalue Poisson problem, Internal Report M.I.P., Universit\u00e9 Paul Sabatier, Toulouse (1996), submitted."},{"key":"2","doi-asserted-by":"crossref","unstructured":"[ABDG] C. Amrouche, C. Bernardi, M. Dauge, V. Girault \u2014 Vector potentials in three-dimensional non-smooth domains, Math. Methods Applied Sci. 21 (1998), 823\u2013864.","DOI":"10.1002\/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1006\/jcph.1993.1214","article-title":"On a finite-element method for solving the three-dimensional Maxwell equations","volume":"109","author":"Assous, F.","year":"1993","journal-title":"J. Comput. 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Grundmann \u2014 Approximation of the wave and electromagnetic equations by spectral methods, SIAM J. Scient. Comput. 20 (1999), 13\u201332.","DOI":"10.1137\/S1064827595294344"},{"key":"7","isbn-type":"print","first-page":"27","article-title":"Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube","author":"Bernardi, Christine","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/082479320X"},{"key":"8","series-title":"Handbook of Numerical Analysis, V","isbn-type":"print","volume-title":"Handbook of numerical analysis. Vol. V","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/044482278X"},{"key":"9","unstructured":"[Bo] A. Bossavit \u2014 Electromagn\u00e9tisme en vue de la mod\u00e9lisation, \u201cMath\u00e9matiques et Applications\u201d 14, Springer-Verlag (1993)."},{"issue":"4","key":"10","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1002\/mma.1670120406","article-title":"A remark on the regularity of solutions of Maxwell\u2019s equations on Lipschitz domains","volume":"12","author":"Costabel, Martin","year":"1990","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"issue":"9","key":"11","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1016\/S0764-4442(97)87876-7","article-title":"Singularit\u00e9s des \u00e9quations de Maxwell dans un poly\u00e8dre","volume":"324","author":"Costabel, Martin","year":"1997","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. 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