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We prove the convergence of the approximate solution to the unique entropy solution of the problem by using compensated compactness arguments.<\/jats:p>","DOI":"10.1137\/070684082","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T19:23:53Z","timestamp":1204745033000},"page":"1060-1078","source":"Crossref","is-referenced-by-count":7,"title":["A Spectral Viscosity Method Based on Hermite Functions for Nonlinear Conservation Laws"],"prefix":"10.1137","volume":"46","author":[{"given":"Juli\u00e1n","family":"Aguirre","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Judith","family":"Rivas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.09.013"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1993-1185240-3"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(87)90001-0"},{"key":"R4","unstructured":"L. C. Evans,\n                      Weak Convergence Methods for Nonlinear Partial Differential Equations\n                      , American Mathematical Society, Providence, RI, 1988."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-01-01365-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1094949-X"},{"key":"R7","unstructured":"E. Godlewski and P. A. Raviart,\n                      Hyperbolic Systems of Conservation Laws\n                      , Societ\u00e9 de Math\u00e9matiques Appliqu\u00e9es et Industrielles, Paris, 1991."},{"key":"R8","doi-asserted-by":"crossref","unstructured":"D. Gottlieb and S. A. Orszag,\n                      Numerical Analysis of Spectral Methods: Theory and Applications\n                      , SIAM-CBMS, Philadelphia, 1977.","DOI":"10.1137\/1.9781611970425"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022892132249"},{"key":"R10","unstructured":"L. H\u00f6rmander,\n                      Lectures on Nonlinear Hyperbolic Differential Equations\n                      , Springer\u2013Verlag, Berlin, Heidelberg, 1997."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"R. J. Leveque,\n                      Numerical methods for conservation laws\n                      , in Lectures in Mathematics ETH Z\u00fcrich, Birkh\u00e4user-Verlag, Basel, 1992.","DOI":"10.1007\/978-3-0348-8629-1"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995293900"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903421278"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0730016"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0726047"},{"key":"R16","unstructured":"M. B. P\u00e9rez Pinilla,\n                      Un m\u00e9todo espectral basado en funciones de Hermite para la resoluci\u00f3n num\u00e9rica de algunas ecuaciones del calor semilineales\n                      , Ph.D. thesis, Universidad del Pa\u00eds Vasco, Bilbao, 1997."},{"key":"R17","unstructured":"W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,\n                      Numerical Recipes in C\n                      , Cambridge University Press, Cambridge, 1992."},{"key":"R18","unstructured":"J. Rivas,\n                      Filtered Hermite Approximations\n                      , preprint."},{"key":"R19","unstructured":"D. Serre,\n                      Syst\u00e8mes de Lois de Conservation\n                      II:\n                      Structures G\u00e9om\u00e9triques, Oscillations et Probl\u00e8mes Mixtes\n                      , Diderot Editeur, Paris, 1996."},{"key":"R20","unstructured":"G. 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Sci."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070684082","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:12:40Z","timestamp":1787325160000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070684082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070684082"],"URL":"https:\/\/doi.org\/10.1137\/070684082","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}