{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:33Z","timestamp":1747198053242,"version":"3.40.5"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1912646"],"award-info":[{"award-number":["1912646"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["11180284"],"award-info":[{"award-number":["11180284"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present a <jats:italic>new<\/jats:italic> class of discontinuous Galerkin methods for the space discretization of the time-dependent Maxwell equations whose main feature is the use of <jats:italic>time derivatives<\/jats:italic> and\/or <jats:italic>time integrals<\/jats:italic> in the <jats:italic>stabilization<\/jats:italic> part of their numerical traces.\nThese numerical traces are chosen in such a way that the resulting semidiscrete schemes exactly conserve a discrete version of the energy.\nWe introduce four model ways of achieving this and show that, when using the mid-point rule to march in time, the fully discrete schemes also conserve the discrete energy.\nMoreover, we propose a new three-step technique to devise fully discrete schemes of arbitrary order of accuracy which conserve the energy in time.\nThe first step consists in transforming the semidiscrete scheme into a Hamiltonian dynamical system.\nThe second step consists in applying a symplectic time-marching method to this dynamical system in order to guarantee that the resulting fully discrete method conserves the discrete energy in time.\nThe third and last step consists in reversing the above-mentioned transformation to rewrite the fully discrete scheme in terms of the original variables.<\/jats:p>","DOI":"10.1515\/cmam-2021-0215","type":"journal-article","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T20:01:05Z","timestamp":1652990465000},"page":"775-796","source":"Crossref","is-referenced-by-count":3,"title":["Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics"],"prefix":"10.1515","volume":"22","author":[{"given":"Bernardo","family":"Cockburn","sequence":"first","affiliation":[{"name":"School of Mathematics , University of Minnesota , Minneapolis , MN 55455 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shukai","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Wisconsin-Madison , Madison , WI 53706 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8175-1831","authenticated-orcid":false,"given":"Manuel A.","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Instituto de Ingenier\u00eda Matem\u00e1tica y Computacional , Facultad de Matem\u00e1ticas y Escuela de Ingenier\u00eda , Pontificia Universidad Cat\u00f3lica de Chile , Santiago , Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"key":"2023033113381517780_j_cmam-2021-0215_ref_001","doi-asserted-by":"crossref","unstructured":"M. Ainsworth,\nDispersive and dissipative behaviour of high order discontinuousGalerkin finite element methods,\nJ. Comput. Phys. 198 (2004), no. 1, 106\u2013130.","DOI":"10.1016\/j.jcp.2004.01.004"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_002","doi-asserted-by":"crossref","unstructured":"T. S. Brown, S. Du, H. Eruslu and F.-J. Sayas,\nAnalysis of models for viscoelastic wave propagation,\nAppl. Math. Nonlinear Sci. 3 (2018), no. 1, 55\u201396.","DOI":"10.21042\/AMNS.2018.1.00006"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_003","doi-asserted-by":"crossref","unstructured":"B. Cockburn,\nThe pursuit of a dream, Francisco Javier Sayas and the HDG methods,\nSeMA J. 79 (2022), no. 1, 37\u201356.","DOI":"10.1007\/s40324-021-00273-y"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_004","doi-asserted-by":"crossref","unstructured":"B. Cockburn, Z. Fu, A. Hungria, L. Ji, M. A. S\u00e1nchez and F.-J. Sayas,\nStormer\u2013Numerov HDG methods for acoustic waves,\nJ. Sci. Comput. 75 (2018), no. 2, 597\u2013624.","DOI":"10.1007\/s10915-017-0547-z"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_005","doi-asserted-by":"crossref","unstructured":"B. Cockburn, J. Gopalakrishnan and R. Lazarov,\nUnified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems,\nSIAM J. Numer. Anal. 47 (2009), no. 2, 1319\u20131365.","DOI":"10.1137\/070706616"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_006","doi-asserted-by":"crossref","unstructured":"B. Cockburn, N. C. Nguyen and J. Peraire,\nHDG methods for hyperbolic problems,\nHandbook of Numerical Methods for Hyperbolic Problems,\nHandb. Numer. Anal. 17,\nElsevier\/North-Holland, Amsterdam (2016), 173\u2013197.","DOI":"10.1016\/bs.hna.2016.07.001"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_007","doi-asserted-by":"crossref","unstructured":"B. Cockburn and V. Quenneville-B\u00e9lair,\nUniform-in-time superconvergence of the HDG methods for the acoustic wave equation,\nMath. Comp. 83 (2014), no. 285, 65\u201385.","DOI":"10.1090\/S0025-5718-2013-02743-3"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_008","doi-asserted-by":"crossref","unstructured":"S. Du and F.-J. Sayas,\nA unified error analysis of hybridizable discontinuous Galerkin methods for the static Maxwell equations,\nSIAM J. Numer. Anal. 58 (2020), no. 2, 1367\u20131391.","DOI":"10.1137\/19M1290966"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_009","doi-asserted-by":"crossref","unstructured":"G. Fu and C.-W. Shu,\nOptimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems,\nJ. Comput. Phys. 394 (2019), 329\u2013363.","DOI":"10.1016\/j.jcp.2019.05.050"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_010","doi-asserted-by":"crossref","unstructured":"Z. Fu, L. F. Gatica and F.-J. Sayas,\nAlgorithm 949: MATLAB tools for HDG in three dimensions,\nACM Trans. Math. Software 41 (2015), no. 3, Article ID 20.","DOI":"10.1145\/2658992"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_011","doi-asserted-by":"crossref","unstructured":"J. Gopalakrishnan, M. Solano and F. Vargas,\nDispersion analysis of HDG methods,\nJ. Sci. Comput. 77 (2018), no. 3, 1703\u20131735.","DOI":"10.1007\/s10915-018-0781-z"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_012","doi-asserted-by":"crossref","unstructured":"A. Hungria, D. Prada and F. J. Sayas,\nHDG methods for elastodynamics,\nComput. Math. Appl. 74 (2017), 2671\u20132690.","DOI":"10.1016\/j.camwa.2017.08.016"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_013","doi-asserted-by":"crossref","unstructured":"N. C. Nguyen, J. Peraire and B. Cockburn,\nHigh-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics,\nJ. Comput. Phys. 230 (2011), no. 10, 3695\u20133718.","DOI":"10.1016\/j.jcp.2011.01.035"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_014","doi-asserted-by":"crossref","unstructured":"N. C. Nguyen, J. Peraire and B. Cockburn,\nHybridizable discontinuous Galerkin methods for the time-harmonic Maxwell\u2019s equations,\nJ. Comput. Phys. 230 (2011), no. 19, 7151\u20137175.","DOI":"10.1016\/j.jcp.2011.05.018"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_015","doi-asserted-by":"crossref","unstructured":"M. A. S\u00e1nchez, C. Ciuca, N. C. Nguyen, J. Peraire and B. Cockburn,\nSymplectic Hamiltonian HDG methods for wave propagation phenomena,\nJ. Comput. Phys. 350 (2017), 951\u2013973.","DOI":"10.1016\/j.jcp.2017.09.010"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_016","doi-asserted-by":"crossref","unstructured":"M. A. S\u00e1nchez, B. Cockburn, N.-C. Nguyen and J. Peraire,\nSymplectic Hamiltonian finite element methods for linear elastodynamics,\nComput. Methods Appl. Mech. Engrg. 381 (2021), Paper No. 113843.","DOI":"10.1016\/j.cma.2021.113843"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_017","doi-asserted-by":"crossref","unstructured":"J. M. Sanz-Serna,\nSymplectic Runge\u2013Kutta and related methods: Recent results,\nPhys. D 60 (1992), 293\u2013302.","DOI":"10.1016\/0167-2789(92)90245-I"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_018","doi-asserted-by":"crossref","unstructured":"F.-J. Sayas, T. S. Brown and M. E. Hassell,\nVariational Techniques for Elliptic Partial Differential Equations: Theoretical Tools and Advanced Applications,\nCRC Press, Boca Raton, 2019.","DOI":"10.1201\/9780429507069"},{"key":"2023033113381517780_j_cmam-2021-0215_ref_019","doi-asserted-by":"crossref","unstructured":"M. Stanglmeier, N. C. Nguyen, J. Peraire and B. Cockburn,\nAn explicit hybridizable discontinuous Galerkin method for the acoustic wave equation,\nComput. Methods Appl. Mech. Engrg. 300 (2016), 748\u2013769.","DOI":"10.1016\/j.cma.2015.12.003"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0215\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0215\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T18:45:19Z","timestamp":1680288319000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0215\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,20]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,3,26]]},"published-print":{"date-parts":[[2022,10,1]]}},"alternative-id":["10.1515\/cmam-2021-0215"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2021-0215","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2022,5,20]]}}}