{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:51:53Z","timestamp":1776786713819,"version":"3.51.2"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"260","license":[{"start":{"date-parts":[[2008,4,20]],"date-time":"2008-04-20T00:00:00Z","timestamp":1208649600000},"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                    In this paper, we present the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">hp<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -convergence analysis of a non-dissipative high-order discontinuous Galerkin method on unstructured hexahedral meshes using a mass-lumping technique to solve the time-dependent Maxwell equations. In particular, we underline the spectral convergence of the method (in the sense that when the solutions and the data are very smooth, the discretization is of unlimited order). Moreover, we see that the choice of a non-standard approximate space (for a discontinuous formulation) with the absence of dissipation can imply a loss of spatial convergence. Finally we present a numerical result which seems to confirm this property.\n                  <\/p>","DOI":"10.1090\/s0025-5718-07-01991-6","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T07:46:03Z","timestamp":1185435963000},"page":"1801-1832","source":"Crossref","is-referenced-by-count":16,"title":["HP a-priori error estimates for a non-dissipative spectral discontinuous Galerkin method to solve the Maxwell equations in the time domain"],"prefix":"10.1090","volume":"76","author":[{"given":"S.","family":"Pernet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"X.","family":"Ferrieres","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2007,4,20]]},"reference":[{"key":"1","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"key":"2","unstructured":"Achdou Yves, The Finite Element Methods, www.ann.jussieu.fr\/achdou\/enseignement."},{"key":"3","unstructured":"Malika Remaki, M\u00e9thodes num\u00e9riques pour les \u00e9quations de Maxwell instationnnaires en Milieu h\u00e9t\u00e9rog\u00e8ne, Doctorat de Math\u00e9matiques Appliqu\u00e9es de l\u2019Ecole Nationale des Ponts et Chauss\u00e9es, 1999."},{"key":"4","series-title":"Scientific Computation","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04823-8","volume-title":"Higher-order numerical methods for transient wave equations","author":"Cohen, Gary C.","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/354041598X"},{"key":"5","doi-asserted-by":"crossref","unstructured":"K.S. 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