{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:46:58Z","timestamp":1776872818673,"version":"3.51.2"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-20-1-0055"],"award-info":[{"award-number":["FA9550-20-1-0055"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010246","name":"Postdoctoral Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["KYCX21_0028"],"award-info":[{"award-number":["KYCX21_0028"]}],"id":[{"id":"10.13039\/501100010246","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071214"],"award-info":[{"award-number":["12071214"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671199"],"award-info":[{"award-number":["11671199"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2010107"],"award-info":[{"award-number":["DMS-2010107"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1137\/21m1435495","type":"journal-article","created":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T18:21:48Z","timestamp":1657736508000},"page":"1741-1773","source":"Crossref","is-referenced-by-count":9,"title":["L$^2$ Error Estimate to Smooth Solutions of High Order Runge--Kutta Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws with and without Sonic Points"],"prefix":"10.1137","volume":"60","author":[{"given":"Jingqi","family":"Ai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7720-9564","authenticated-orcid":true,"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1796-7042","authenticated-orcid":true,"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2022,7,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2015.08.021"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/090757940"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2016026"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3141"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1115\/1.3424474"},{"key":"atypb7","first-page":"545","volume":"54","author":"Cockburn B.","year":"1990","journal-title":"Math. Comp."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90183-6"},{"key":"atypb9","first-page":"411","volume":"52","author":"Cockburn B.","year":"1989","journal-title":"Math. Comp."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1991250303371"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5892"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1994-1223232-7"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0815828-4"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2009.01.007"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-208350-1.50008-X"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-018-0831-6"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/19M1243798"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2014063"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3022"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/110857635"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.07.011"},{"key":"atypb22","volume-title":"Los Alamos Scientific Laboratory report LA-UR-73-479","author":"Reed W. H.","year":"1973"},{"key":"atypb23","first-page":"354","volume-title":"Acad. Sci. USSR Siberian Branch","author":"Richtmyer R. D.","year":"1963"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-01818-8_2"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/b79761"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.08.007"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-020-01274-1"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.10.043"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/19M1280077"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/18M1230700"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-022-01793-z"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902404182"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/040620382"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1137\/090771363"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T18:24:13Z","timestamp":1661970253000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1435495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,13]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1137\/21M1435495"],"URL":"https:\/\/doi.org\/10.1137\/21m1435495","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,13]]}}}