{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T04:44:48Z","timestamp":1783485888992,"version":"3.55.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2008,9,18]],"date-time":"2008-09-18T00:00:00Z","timestamp":1221696000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2009,7]]},"DOI":"10.1007\/s10915-008-9247-z","type":"journal-article","created":{"date-parts":[[2008,9,17]],"date-time":"2008-09-17T13:53:46Z","timestamp":1221659626000},"page":"257-272","source":"Crossref","is-referenced-by-count":80,"title":["Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation"],"prefix":"10.1007","volume":"40","author":[{"given":"Marcus J.","family":"Grote","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dominik","family":"Sch\u00f6tzau","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2008,9,18]]},"reference":[{"key":"9247_CR1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10915-005-9044-x","volume":"27","author":"M. Ainsworth","year":"2006","unstructured":"Ainsworth,\u00a0M., Monk,\u00a0P., Muniz,\u00a0W.: Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. J.\u00a0Sci. Comput. 27, 5\u201340 (2006)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9247_CR2","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D.N. Arnold","year":"2002","unstructured":"Arnold,\u00a0D.N., Brezzi,\u00a0F., Cockburn,\u00a0B., Marini,\u00a0L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749\u20131779 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR3","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1137\/0713048","volume":"13","author":"G.A. Baker","year":"1976","unstructured":"Baker,\u00a0G.A.: Error estimates for finite element methods for second-order hyperbolic equations. SIAM J. Numer. Anal. 13, 564\u2013576 (1976)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR4","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1051\/m2an\/1979130302011","volume":"13","author":"G.A. Baker","year":"1979","unstructured":"Baker,\u00a0G.A., Dougalis,\u00a0V.A., Serbin,\u00a0S.M.: High order accurate two-step approximations for hyperbolic equations. RAIRO. Mod\u00e9l. Math. Anal. Num\u00e9r. 13, 201\u2013226 (1979)","journal-title":"RAIRO. Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"9247_CR5","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1137\/S0036142998345499","volume":"37","author":"E. B\u00e9cache","year":"2000","unstructured":"B\u00e9cache,\u00a0E., Joly,\u00a0P., Tsogka,\u00a0C.: An analysis of new mixed finite elements for the approximation of wave propagation problems. SIAM J. Numer. Anal. 37, 1053\u20131084 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR6","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"Ciarlet,\u00a0P.G.: The Finite Element Method for Elliptic Problems. North\u2013Holland, Amsterdam (1978)"},{"key":"9247_CR7","series-title":"Lect. Notes Comput. Sci. Engrg.","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/978-3-662-03882-6_2","volume-title":"High-Order Methods for Computational Physics","author":"B. Cockburn","year":"1999","unstructured":"Cockburn,\u00a0B.: Discontinuous Galerkin methods for convection-dominated problems. In: Barth,\u00a0T., Deconink,\u00a0H. (eds.) High-Order Methods for Computational Physics. Lect. Notes Comput. Sci. Engrg., vol.\u00a09, pp.\u00a069\u2013224. Springer, Berlin (1999)"},{"key":"9247_CR8","series-title":"Lect. Notes Comput. Sci. Engrg.","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-642-59721-3_1","volume-title":"Discontinuous Galerkin Methods: Theory, Computation and Applications","author":"B. Cockburn","year":"2000","unstructured":"Cockburn,\u00a0B., Karniadakis,\u00a0G.E., Shu,\u00a0C.-W.: The development of discontinuous Galerkin methods. In: Cockburn,\u00a0B., Karniadakis,\u00a0G.E., Shu,\u00a0C.-W. (eds.) Discontinuous Galerkin Methods: Theory, Computation and Applications. Lect. Notes Comput. Sci. Engrg., vol.\u00a011, pp.\u00a03\u201350. Springer, Berlin (2000)"},{"key":"9247_CR9","first-page":"411","volume":"52","author":"B. Cockburn","year":"1989","unstructured":"Cockburn,\u00a0B., Shu,\u00a0C.-W.: TVB Runge\u2013Kutta local projection discontinuous Galerkin method for conservation laws II: General framework. Math. Comput. 52, 411\u2013435 (1989)","journal-title":"Math. Comput."},{"key":"9247_CR10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B. Cockburn","year":"2001","unstructured":"Cockburn,\u00a0B., Shu,\u00a0C.-W.: Runge\u2013Kutta discontinuous Galerkin methods for convection\u2013dominated problems. J.\u00a0Sci. Comput. 16, 173\u2013261 (2001)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9247_CR11","doi-asserted-by":"crossref","first-page":"2047","DOI":"10.1137\/S0036142997329554","volume":"38","author":"G. Cohen","year":"2001","unstructured":"Cohen,\u00a0G., Joly,\u00a0P., Roberts,\u00a0J.E., Tordjman,\u00a0N.: Higher order triangular finite elements with mass lumping for the wave equation. SIAM J. Numer. Anal. 38, 2047\u20132078 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR12","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0045-7825(90)90165-I","volume":"82","author":"L.C. Cowsar","year":"1990","unstructured":"Cowsar,\u00a0L.C., Dupont,\u00a0T.F., Wheeler,\u00a0M.F.: A-priori estimates for mixed finite element methods for the wave equations. Comput. Methods Appl. Mech. Eng. 82, 205\u2013222 (1990)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9247_CR13","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1137\/0733026","volume":"33","author":"L.C. Cowsar","year":"1996","unstructured":"Cowsar,\u00a0L.C., Dupont,\u00a0T.F., Wheeler,\u00a0M.F.: A-priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions. SIAM J. Numer. Anal. 33, 492\u2013504 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR14","doi-asserted-by":"crossref","unstructured":"Diaz,\u00a0J., Grote,\u00a0M.J.: Energy conserving explicit local time-stepping for second-order wave equations. SIAM J. Sci. Comput. (in press)","DOI":"10.1137\/070709414"},{"key":"9247_CR15","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1137\/0710073","volume":"10","author":"T. Dupont","year":"1973","unstructured":"Dupont,\u00a0T.: L 2-estimates for Galerkin methods for second-order hyperbolic equations. SIAM J. Numer. Anal. 10, 880\u2013889 (1973)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9247_CR16","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1137\/S0036142997329463","volume":"36","author":"R.S. Falk","year":"1999","unstructured":"Falk,\u00a0R.S., Richter,\u00a0G.R.: Explicit finite element methods for symmetric hyperbolic equations. SIAM J. Numer. Anal. 36(3), 935\u2013952 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR17","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1090\/S0025-5718-96-00685-0","volume":"66","author":"D.A. French","year":"1996","unstructured":"French,\u00a0D.A., Peterson,\u00a0T.E.: A continuous space-time finite element method for the wave equation. Math. Comput. 66, 491\u2013506 (1996)","journal-title":"Math. Comput."},{"key":"9247_CR18","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1137\/0713046","volume":"13","author":"E. Gekeler","year":"1976","unstructured":"Gekeler,\u00a0E.: Linear multi-step methods and Galerkin procedures for initial boundary value problems. SIAM J. Numer. Anal. 13, 536\u2013548 (1976)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR19","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1051\/m2an\/1988220202431","volume":"22","author":"T. Geveci","year":"1988","unstructured":"Geveci,\u00a0T.: On the application of mixed finite methods to the wave equation. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 22, 243\u2013250 (1988)","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"9247_CR20","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1137\/05063194X","volume":"44","author":"M.J. Grote","year":"2006","unstructured":"Grote,\u00a0M.J., Schneebeli,\u00a0A., Sch\u00f6tzau,\u00a0D.: Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44, 2408\u20132431 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9247_CR21","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.cam.2006.01.044","volume":"204","author":"M.J. Grote","year":"2007","unstructured":"Grote,\u00a0M.J., Schneebeli,\u00a0A., Sch\u00f6tzau,\u00a0D.: Interior penalty discontinuous Galerkin method for Maxwell\u2019s equations: Energy norm error estimates. J.\u00a0Comput. Appl. Math. 204, 375\u2013386 (2007)","journal-title":"J.\u00a0Comput. Appl. Math."},{"key":"9247_CR22","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1093\/imanum\/drm038","volume":"28","author":"M.J. Grote","year":"2008","unstructured":"Grote,\u00a0M.J., Schneebeli,\u00a0A., Sch\u00f6tzau,\u00a0D.: Interior penalty discontinuous Galerkin method for Maxwell\u2019s equations: Optimal L 2-norm error estimates. IMA J. Numer. Anal. 28, 440\u2013468 (2008)","journal-title":"IMA J. Numer. Anal."},{"key":"9247_CR23","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1006\/jcph.2002.7118","volume":"181","author":"J.S. Hesthaven","year":"2002","unstructured":"Hesthaven,\u00a0J.S., Warburton,\u00a0T.: Nodal high-order methods on unstructured grids I: Time-domain solution of Maxwell\u2019s equations. J.\u00a0Comput. Phys. 181, 186\u2013221 (2002)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9247_CR24","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1015180009979","volume":"17","author":"P. Houston","year":"2002","unstructured":"Houston,\u00a0P., Jensen,\u00a0M., S\u00fcli,\u00a0E.: hp-discontinuous Galerkin finite element methods with least-squares stabilization. J.\u00a0Sci. Comput. 17, 3\u201325 (2002)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9247_CR25","volume-title":"The Finite Element Method: Linear Static and Dynamic Finite Element Analysis","author":"T. Hughes","year":"1987","unstructured":"Hughes,\u00a0T.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall, New York (1987)"},{"key":"9247_CR26","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s10915-004-4132-5","volume":"22\u201323","author":"P. Monk","year":"2005","unstructured":"Monk,\u00a0P., Richter,\u00a0G.R.: A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media. J.\u00a0Sci. Comput. 22\u201323, 443\u2013477 (2005)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9247_CR27","unstructured":"Rivi\u00e8re,\u00a0B., Wheeler,\u00a0M.F.: Discontinuous finite element methods for acoustic and elastic wave problems I: Semi-discrete error estimates. Technical Report 01-02, TICAM, UT Austin (2001)"},{"key":"9247_CR28","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1090\/conm\/329\/05862","volume-title":"ICM2002-Beijing Satellite Conference on Scientific Computing","author":"B. Rivi\u00e8re","year":"2003","unstructured":"Rivi\u00e8re,\u00a0B., Wheeler,\u00a0M.F.: Discontinuous finite element methods for acoustic and elastic wave problems. In: ICM2002-Beijing Satellite Conference on Scientific Computing. Contemporary Mathematics, vol.\u00a0329, pp.\u00a0271\u2013282. Am. Math. Soc., Providence (2003)"},{"key":"9247_CR29","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0045-7825(93)90046-Z","volume":"103","author":"A. Safjan","year":"1993","unstructured":"Safjan,\u00a0A., Oden,\u00a0J.T.: High-order Taylor-Galerkin and adaptive h\u2212p methods for second-order hyperbolic systems: Applications to elastodynamics. Comput. Methods Appl. Mech. Eng. 103, 187\u2013230 (1993)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9247_CR30","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/0908026","volume":"8","author":"G.R. Shubin","year":"1987","unstructured":"Shubin,\u00a0G.R., Bell,\u00a0J.: A modified equation approach to constructing fourth-order methods for acoustic wave propagation. SIAM J. Sci. Comput. 8, 135\u2013151 (1987)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9247-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-008-9247-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9247-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:41:30Z","timestamp":1559464890000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-008-9247-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,18]]},"references-count":30,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["9247"],"URL":"https:\/\/doi.org\/10.1007\/s10915-008-9247-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,18]]}}}