{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T17:27:19Z","timestamp":1791134839474,"version":"4.1.0"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We show that the approximation given by the original discontinuous Galerkin method for the transport-reaction equation in d space dimensions is optimal provided the meshes are suitably chosen: the $L^2$-norm of the error is of order $k+1$ when the method uses polynomials of degree k. These meshes are not necessarily conforming and do not satisfy any uniformity condition; they are required only to be made of simplexes, each of which has a unique outflow face. We also find a new, element-by-element postprocessing of the derivative in the direction of the flow which superconverges with order $k+1$.<\/jats:p>","DOI":"10.1137\/060677215","type":"journal-article","created":{"date-parts":[[2008,3,21]],"date-time":"2008-03-21T18:06:56Z","timestamp":1206122816000},"page":"1250-1265","source":"Crossref","is-referenced-by-count":81,"title":["Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes"],"prefix":"10.1137","volume":"46","author":[{"given":"Bernardo","family":"Cockburn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00502-9"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0719052"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/fld.562"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"F. Brezzi and M. Fortin,\n                      Mixed and Hybrid Finite Element Methods\n                      , Springer-Verlag, New York, 1991.","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"P. Ciarlet,\n                      The Finite Element Method for Elliptic Problems\n                      , North-Holland, Amsterdam, 1978.","DOI":"10.1115\/1.3424474"},{"key":"R7","unstructured":"B. Cockburn, B. Dong, and J. Guzm\u00e1n,\n                      A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems\n                      , Math. Comp., accepted."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-04-01718-1"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2005.07.003"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s002110200392"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1163\/156939506776382157"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0815828-4"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"P. Lesaint and P.A. Raviart,\n                      On a finite element method for solving the neutron transport equation\n                      , in Mathematical Aspects for Finite Elements in Partial Differential Equations, C. de Boor, ed., Academic Press, New York, 1974, pp. 89\u2013123.","DOI":"10.1016\/B978-0-12-208350-1.50008-X"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0728006"},{"key":"R15","unstructured":"W. Reed and T. Hill,\n                      Triangular Mesh Methods for the Neutron Transport Equation\n                      , Technical report LA-UR-73-479, Los Alamos National Laboratory, Los Alamos, NM, 1973."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1988-0917819-3"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2426(199601)12:1<123::AID-NUM7>3.0.CO;2-U"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060677215","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:13:29Z","timestamp":1787325209000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060677215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060677215"],"URL":"https:\/\/doi.org\/10.1137\/060677215","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}