{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T04:45:48Z","timestamp":1776919548715,"version":"3.51.2"},"reference-count":45,"publisher":"American Mathematical Society (AMS)","issue":"243","license":[{"start":{"date-parts":[[2003,10,18]],"date-time":"2003-10-18T00:00:00Z","timestamp":1066435200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in a low-frequency regime is introduced and analyzed. Topologically nontrivial domains and heterogeneous media are considered, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, derived by introducing suitable auxiliary variables and so-called numerical fluxes. An\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                    -analysis is carried out and error estimates that are optimal in the meshsize\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and slightly suboptimal in the approximation degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are obtained.\n                  <\/p>","DOI":"10.1090\/s0025-5718-02-01471-0","type":"journal-article","created":{"date-parts":[[2003,4,18]],"date-time":"2003-04-18T13:09:02Z","timestamp":1050671342000},"page":"1179-1214","source":"Crossref","is-referenced-by-count":90,"title":["The \u210e\ud835\udc5d-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations"],"prefix":"10.1090","volume":"72","author":[{"given":"Ilaria","family":"Perugia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dominik","family":"Sch\u00f6tzau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2002,10,18]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1142\/S0218202599000245","article-title":"A mathematical justification of the low-frequency heterogeneous time-harmonic Maxwell equations","volume":"9","author":"Alonso, Ana","year":"1999","journal-title":"Math. 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