{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:12:08Z","timestamp":1776845528683,"version":"3.51.2"},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401417"],"award-info":[{"award-number":["11401417"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11225107"],"award-info":[{"award-number":["11225107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper proposes and analyzes a hybridizable discontinuous Galerkin (HDG)\nmethod for the three-dimensional time-harmonic Maxwell equations coupled with\nthe impedance boundary condition in the case of high wave number.\nIt is proved that the HDG method is absolutely stable for all wave numbers <jats:inline-formula id=\"j_cmam-2016-0021_eq_9999_w2aab3b7e2803b1b6b1aab1c13b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>\u03ba<\/m:mi>\n                              <m:mo>&gt;<\/m:mo>\n                              <m:mn>0<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>${\\kappa&gt;0}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>\nin the sense that no mesh constraint is required for the stability. A wave-number-explicit stability constant is also obtained.\nThis is done by choosing a specific penalty parameter and using a PDE duality argument.\nUtilizing the stability estimate and a non-standard technique, the error estimates\nin both the energy-norm and the <jats:inline-formula id=\"j_cmam-2016-0021_eq_9998_w2aab3b7e2803b1b6b1aab1c13b1b3Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>\ud835\udc0b<\/m:mi>\n                              <m:mn>2<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:tex-math>${\\mathbf{L}^{2}}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norm are obtained for the HDG method.\nNumerical experiments are provided to validate the theoretical results and\nto gauge the performance of the proposed HDG method.<\/jats:p>","DOI":"10.1515\/cmam-2016-0021","type":"journal-article","created":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T10:01:31Z","timestamp":1464775291000},"page":"429-445","source":"Crossref","is-referenced-by-count":18,"title":["A Hybridizable Discontinuous Galerkin Method for the Time-Harmonic Maxwell Equations with High Wave Number"],"prefix":"10.1515","volume":"16","author":[{"given":"Xiaobing","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA"}]},{"given":"Peipei","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematics Sciences, Soochow University, Suzhou 215006, P.\u2009R. China"}]},{"given":"Xuejun","family":"Xu","sequence":"additional","affiliation":[{"name":"LSEC, Institute of Computational Mathematics and Scientific\/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100190; and Department of Mathematics, Tongji University, Shanghai, P.\u2009R. China"}]}],"member":"374","published-online":{"date-parts":[[2016,6,1]]},"reference":[{"key":"2023033112444852702_j_cmam-2016-0021_ref_001_w2aab3b7e2803b1b6b1ab2ab1Aa","unstructured":"Adams R.,\nSobolev Spaces,\nAcademic Press, New York, 1975."},{"key":"2023033112444852702_j_cmam-2016-0021_ref_002_w2aab3b7e2803b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"Amrouche C., Bernardi C., Dauge M. and Girault V.,\nVector potentials in three-dimensional non-smooth domains,\nMath. Methods Appl. 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