{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T03:43:50Z","timestamp":1775015030271,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"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":[[2007,9,25]]},"DOI":"10.1007\/s10915-007-9149-5","type":"journal-article","created":{"date-parts":[[2007,8,31]],"date-time":"2007-08-31T00:37:07Z","timestamp":1188520627000},"page":"183-208","source":"Crossref","is-referenced-by-count":16,"title":["Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems"],"prefix":"10.1007","volume":"33","author":[{"given":"E.","family":"Burman","sequence":"first","affiliation":[]},{"given":"B.","family":"Stamm","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,9,1]]},"reference":[{"issue":"3","key":"9149_CR1","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/PL00005475","volume":"89","author":"F. Brezzi","year":"2001","unstructured":"Brezzi, F., Fortin, M.: A minimal stabilisation procedure for mixed finite element methods. Numer. Math. 89(3), 457\u2013491 (2001). MR1864427 (2002h:65176)","journal-title":"Numer. Math."},{"issue":"12","key":"9149_CR2","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1142\/S0218202504003866","volume":"14","author":"F. Brezzi","year":"2004","unstructured":"Brezzi, F., Marini, L.D., S\u00fcli, E.: Discontinuous Galerkin methods for first-order hyperbolic problems. Math. Models Methods Appl. Sci. 14(12), 1893\u20131903 (2004). MR2108234 (2005m:65259)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"25\u201328","key":"9149_CR3","doi-asserted-by":"crossref","first-page":"3293","DOI":"10.1016\/j.cma.2005.06.015","volume":"195","author":"F. Brezzi","year":"2006","unstructured":"Brezzi, F., Cockburn, B., Marini, L.D., S\u00fcli, E.: Stabilization mechanisms in discontinuous Galerkin finite element methods. Comput. Methods Appl. Mech. Eng. 195(25\u201328), 3293\u20133310 (2006). MR2220920","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"9149_CR4","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1137\/S0036142903437374","volume":"43","author":"E. Burman","year":"2005","unstructured":"Burman, E.: A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty. SIAM J. Numer. Anal. 43(5), 2012\u20132033 (2005) (electronic). MR2192329","journal-title":"SIAM J. Numer. Anal."},{"key":"9149_CR5","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1090\/S0025-5718-07-01951-5","volume":"76","author":"E. Burman","year":"2007","unstructured":"Burman, E., Ern, A.: Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comput. 76, 1119\u20131140 (2007)","journal-title":"Math. Comput."},{"issue":"15\u201316","key":"9149_CR6","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1016\/j.cma.2003.12.032","volume":"193","author":"E. Burman","year":"2004","unstructured":"Burman, E., Hansbo, P.: Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Comput. Methods Appl. Mech. Eng. 193(15\u201316), 1437\u20131453 (2004). MR2068903 (2005d:65186)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9149_CR7","unstructured":"Burman, E., Stamm, B.: Discontinuous and continuous finite element methods with interior penalty for hyperbolic problems. Tech. Report, EPFL-IACS report 17 (2005)"},{"key":"9149_CR8","series-title":"Classics in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719208","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics, vol.\u00a040. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2002). MR1930132"},{"key":"9149_CR9","series-title":"Lect. Notes Comput. Sci. Eng.","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, B.: Discontinuous Galerkin methods for convection-dominated problems. In: High-Order Methods for Computational Physics. Lect. Notes Comput. Sci. Eng., vol. 9, pp. 69\u2013224. Springer, Berlin (1999). MR1712278 (2000f:76095)"},{"issue":"1\u20132","key":"9149_CR10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0377-0427(00)00512-4","volume":"128","author":"B. Cockburn","year":"2001","unstructured":"Cockburn, B.: Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws. J. Comput. Appl. Math. 128(1\u20132), 187\u2013204 (2001). MR1820874 (2001m:65127)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"9149_CR11","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B. Cockburn","year":"2001","unstructured":"Cockburn, B., Shu, C.-W.: Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16(3), 173\u2013261 (2001). MR1873283 (2002i:65099)","journal-title":"J. Sci. Comput."},{"key":"9149_CR12","series-title":"Lecture Notes in Phys.","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BFb0120591","volume-title":"Computing Methods in Applied Sciences","author":"J. Douglas","year":"1976","unstructured":"Douglas, J., Dupont, T.: Interior penalty procedures for elliptic and parabolic Galerkin methods. In: Computing Methods in Applied Sciences, Second Internat. Sympos., Versailles, 1975. Lecture Notes in Phys., vol. 58, pp. 207\u2013216. Springer, Berlin (1976)"},{"issue":"4","key":"9149_CR13","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF01060030","volume":"6","author":"M. Dubiner","year":"1991","unstructured":"Dubiner, M.: Spectral methods on triangles and other domains. J. Sci. Comput. 6(4), 345\u2013390 (1991). MR1154903 (92k:76061)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"9149_CR14","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1137\/050624133","volume":"44","author":"A. Ern","year":"2006","unstructured":"Ern, A., Guermond, J.-L.: Discontinuous Galerkin methods for Friedrichs\u2019 systems. i. General theory. SIAM J. Numer. Anal. 44(2), 753\u2013778 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9149_CR15","volume-title":"Table of Integrals, Series, and Products","author":"I.S. Gradshteyn","year":"1994","unstructured":"Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic, Boston (1994). MR1243179 (94g:00008)"},{"issue":"1","key":"9149_CR16","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1163\/156939506776382157","volume":"14","author":"J. Guzm\u00e1n","year":"2006","unstructured":"Guzm\u00e1n, J.: Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems. J. Numer. Math. 14(1), 41\u201356 (2006). MR2229818 (2007b:65122)","journal-title":"J. Numer. Math."},{"issue":"6","key":"9149_CR17","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1137\/S0036142900374111","volume":"39","author":"P. Houston","year":"2002","unstructured":"Houston, P., Schwab, C., S\u00fcli, E.: Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39(6), 2133\u20132163 (2002) (electronic). MR1897953 (2003d:65108)","journal-title":"SIAM J. Numer. Anal."},{"key":"9149_CR18","unstructured":"Jensen, M.: Discontinuous Galerkin methods for Friedrichs\u2019 systems with irregular solutions. Ph.D. thesis, University of Oxford (2004)"},{"issue":"173","key":"9149_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1986-0815828-4","volume":"46","author":"C. Johnson","year":"1986","unstructured":"Johnson, C., Pitk\u00e4ranta, J.: An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comput. 46(173), 1\u201326 (1986). MR815828 (88b:65109)","journal-title":"Math. Comput."},{"key":"9149_CR20","series-title":"Math. Res. Center, Univ. of Wisconsin-Madison","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/B978-0-12-208350-1.50008-X","volume-title":"Mathematical Aspects of Finite Elements in Partial Differential Equations","author":"P. Lesaint","year":"1974","unstructured":"Lesaint, P., Raviart, P.-A.: On a finite element method for solving the neutron transport equation. In: Mathematical Aspects of Finite Elements in Partial Differential Equations, Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974. Math. Res. Center, Univ. of Wisconsin-Madison, vol. 33, pp. 89\u2013123. Academic, New York (1974). MR0658142 (58 #31918)"},{"key":"9149_CR21","unstructured":"Reed, W.H., Hill, T.R.: Triangular mesh methods for the neutron transport equation, Tech. Report LA-UR-73-479, Los Alamos Scientific Laboratory (1973)"},{"key":"9149_CR22","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03359-3","volume-title":"Galerkin Finite Element Methods for Parabolic Problems","author":"V. Thom\u00e9e","year":"1997","unstructured":"Thom\u00e9e, V.: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol.\u00a025. Springer, Berlin (1997). MR1479170 (98m:65007)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-007-9149-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-007-9149-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-007-9149-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:41:29Z","timestamp":1559450489000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-007-9149-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,9,25]]}},"alternative-id":["9149"],"URL":"https:\/\/doi.org\/10.1007\/s10915-007-9149-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,1]]}}}