{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:12:07Z","timestamp":1776845527500,"version":"3.51.2"},"reference-count":49,"publisher":"American Mathematical Society (AMS)","issue":"281","license":[{"start":{"date-parts":[[2013,7,3]],"date-time":"2013-07-03T00:00:00Z","timestamp":1372809600000},"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                    In this paper, we extend to the time-harmonic Maxwell equations the\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                    \u2013version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia,\n                    <italic>\n                      Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the\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                      -version\n                    <\/italic>\n                    , SIAM J.\u00a0Numer.\u00a0Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02627-5","type":"journal-article","created":{"date-parts":[[2012,7,3]],"date-time":"2012-07-03T12:16:00Z","timestamp":1341317760000},"page":"247-268","source":"Crossref","is-referenced-by-count":68,"title":["Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations"],"prefix":"10.1090","volume":"82","author":[{"given":"Ralf","family":"Hiptmair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Moiola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilaria","family":"Perugia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,7,3]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1137\/S0036142903423460","article-title":"Discrete dispersion relation for \u210e\ud835\udc5d-version finite element approximation at high wave number","volume":"42","author":"Ainsworth, Mark","year":"2004","journal-title":"SIAM J. 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