{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:03:26Z","timestamp":1776769406257,"version":"3.51.2"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"216","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We consider here second-order finite volume methods for one-dimensional scalar conservation laws. We give a method to determine a slope reconstruction satisfying\n                    <italic>all<\/italic>\n                    the\n                    <italic>exact<\/italic>\n                    numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a convergence rate of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Delta x Superscript 1 slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">\n                              \u0394\n                              \n                            <\/mml:mi>\n                            <mml:msup>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Delta x^{1\/2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . It is obtained by a theory of second-order entropic projections involving values at the nodes of the grid and a variant of error estimates, which also gives new results for the first-order Engquist-Osher scheme.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00752-1","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1439-1461","source":"Crossref","is-referenced-by-count":59,"title":["A MUSCL method satisfying all the numerical entropy inequalities"],"prefix":"10.1090","volume":"65","author":[{"given":"F.","family":"Bouchut","sequence":"first","affiliation":[]},{"given":"Ch.","family":"Bourdarias","sequence":"additional","affiliation":[]},{"given":"B.","family":"Perthame","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"6","key":"1","first-page":"619","article-title":"Un exemple de m\u00e9thode MUSCL satisfaisant toutes les in\u00e9galit\u00e9s d\u2019entropie num\u00e9riques","volume":"317","author":"Bouchut, Fran\u00e7ois","year":"1993","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"issue":"6","key":"2","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1137\/0721063","article-title":"Averaged multivalued solutions for scalar conservation laws","volume":"21","author":"Brenier, Yann","year":"1984","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/0022-0396(83)90067-0","article-title":"R\u00e9solution d\u2019\u00e9quations d\u2019\u00e9volution quasilin\u00e9aires en dimension \ud835\udc41 d\u2019espace \u00e0 l\u2019aide d\u2019\u00e9quations lin\u00e9aires en dimension \ud835\udc41+1","volume":"50","author":"Brenier, Yann","year":"1983","journal-title":"J. Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0022-0396","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1137\/0725002","article-title":"The discrete one-sided Lipschitz condition for convex scalar conservation laws","volume":"25","author":"Brenier, Yann","year":"1988","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF01385691","article-title":"Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh","volume":"66","author":"Champier, S.","year":"1993","journal-title":"Numer. 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Yang, Nonlinear wave analysis and convergence of MUSCL schemes, Preprint IMA (1991)."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00752-1\/S0025-5718-96-00752-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00752-1\/S0025-5718-96-00752-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:16:23Z","timestamp":1776719783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00752-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":31,"journal-issue":{"issue":"216","published-print":{"date-parts":[[1996,10]]}},"alternative-id":["S0025-5718-96-00752-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00752-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}