{"id":"https://openalex.org/W4393382168","doi":"https://doi.org/10.1137/22m1524151","title":"An Entropy Stable Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Conservation Laws","display_name":"An Entropy Stable Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Conservation Laws","publication_year":2024,"publication_date":"2024-04-01","ids":{"openalex":"https://openalex.org/W4393382168","doi":"https://doi.org/10.1137/22m1524151"},"language":"en","primary_location":{"id":"doi:10.1137/22m1524151","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1524151","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089825319","display_name":"Yong Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong Liu","raw_affiliation_strings":["LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u2019s Republic of China","LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-1385-0170","affiliations":[{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070178842","display_name":"Jianfang Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianfang Lu","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Canton, Guangdong 510641, People\u2019s Republic of China","School of Mathematics, South China University of Technology, Canton, Guangdong 510641, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Canton, Guangdong 510641, People\u2019s Republic of China","institution_ids":["https://openalex.org/I90610280"]},{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Canton, Guangdong 510641, People's Republic of China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912 USA"],"raw_orcid":"https://orcid.org/0000-0001-7720-9564","affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912 USA","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089825319"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":3.2245,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.9175629,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"A1132","last_page":"A1159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.903111457824707},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5653889775276184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5548732876777649},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5518614649772644},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5088961124420166},{"id":"https://openalex.org/keywords/southern-oscillation","display_name":"Southern oscillation","score":0.49499982595443726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3927909731864929},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3217286169528961},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31281471252441406},{"id":"https://openalex.org/keywords/el-ni\u00f1o-southern-oscillation","display_name":"El Ni\u00f1o Southern Oscillation","score":0.25030919909477234},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.13259315490722656},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.070100337266922},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.06978359818458557},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06453022360801697},{"id":"https://openalex.org/keywords/climatology","display_name":"Climatology","score":0.0612814724445343}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.903111457824707},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5653889775276184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5548732876777649},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5518614649772644},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5088961124420166},{"id":"https://openalex.org/C2993855988","wikidata":"https://www.wikidata.org/wiki/Q14524818","display_name":"Southern oscillation","level":3,"score":0.49499982595443726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3927909731864929},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3217286169528961},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31281471252441406},{"id":"https://openalex.org/C507956050","wikidata":"https://www.wikidata.org/wiki/Q14524818","display_name":"El Ni\u00f1o Southern Oscillation","level":2,"score":0.25030919909477234},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.13259315490722656},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.070100337266922},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.06978359818458557},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06453022360801697},{"id":"https://openalex.org/C49204034","wikidata":"https://www.wikidata.org/wiki/Q52139","display_name":"Climatology","level":1,"score":0.0612814724445343},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1524151","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1524151","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.7300000190734863,"id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G3110018448","display_name":null,"funder_award_id":"12201621","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5683764535","display_name":null,"funder_award_id":"DMS-2010107","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6515063584","display_name":null,"funder_award_id":"11901213","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6537753973","display_name":null,"funder_award_id":"FA9550-20-1-0055","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335892","display_name":"Youth Innovation Promotion Association","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1093977366","https://openalex.org/W1972924431","https://openalex.org/W1973481688","https://openalex.org/W1981017638","https://openalex.org/W1990596161","https://openalex.org/W1995071315","https://openalex.org/W1999399767","https://openalex.org/W2008046188","https://openalex.org/W2008956940","https://openalex.org/W2010222530","https://openalex.org/W2027087330","https://openalex.org/W2039150507","https://openalex.org/W2041983391","https://openalex.org/W2052836614","https://openalex.org/W2053715298","https://openalex.org/W2056167539","https://openalex.org/W2056644251","https://openalex.org/W2059603117","https://openalex.org/W2065978762","https://openalex.org/W2072226973","https://openalex.org/W2078033075","https://openalex.org/W2086888240","https://openalex.org/W2092134511","https://openalex.org/W2104463304","https://openalex.org/W2122177687","https://openalex.org/W2129462040","https://openalex.org/W2132133111","https://openalex.org/W2167278920","https://openalex.org/W2170590789","https://openalex.org/W2409693504","https://openalex.org/W2526384912","https://openalex.org/W2604525805","https://openalex.org/W2605493455","https://openalex.org/W2614749877","https://openalex.org/W2757708288","https://openalex.org/W2768176009","https://openalex.org/W2772909518","https://openalex.org/W2810690184","https://openalex.org/W2895479863","https://openalex.org/W2949414414","https://openalex.org/W2963095461","https://openalex.org/W2963482900","https://openalex.org/W2964287368","https://openalex.org/W2964350974","https://openalex.org/W2977985257","https://openalex.org/W3024549653","https://openalex.org/W3100107498","https://openalex.org/W3100448260","https://openalex.org/W3160041104","https://openalex.org/W4210760027","https://openalex.org/W4232258220","https://openalex.org/W4252060206","https://openalex.org/W4388322678"],"related_works":["https://openalex.org/W1995118522","https://openalex.org/W2726528067","https://openalex.org/W2129573473","https://openalex.org/W2380255313","https://openalex.org/W2952149072","https://openalex.org/W2154700905","https://openalex.org/W2948931127","https://openalex.org/W4288335771","https://openalex.org/W4312002271","https://openalex.org/W2091960656"],"abstract_inverted_index":{".Entropy":[0],"inequalities":[1,36],"are":[2,155,242],"crucial":[3],"to":[4,13,157,168,203,244],"the":[5,15,21,75,88,117,170,175,183,205,208,212,215,218,222,233,246,250,257],"well-posedness":[6],"of":[7,90,207,214,225,252,256],"hyperbolic":[8,109],"conservation":[9,110,260],"laws,":[10],"which":[11],"help":[12],"select":[14],"physically":[16],"meaningful":[17],"one":[18],"from":[19],"among":[20],"infinite":[22],"many":[23],"weak":[24],"solutions.":[25],"Recently,":[26],"several":[27],"high":[28,79,99,118,196],"order":[29,80,100,119,197],"discontinuous":[30],"Galerkin":[31,263],"(DG)":[32],"methods":[33,82],"satisfying":[34],"entropy":[35,101,177,192,209,230,235],"were":[37],"proposed;":[38],"see":[39],"[T.":[40],"Chen":[41,62],"and":[42,63,74,128,143,211,229,249],"C.-W.":[43,64,129,144],"Shu,":[44,65,130,145],"J.":[45,52,54,132,141,147],"Comput.":[46,55],"Phys.,":[47,56],"345":[48],"(2017),":[49],"pp.":[50,59,72,137,152],"427\u2013461;":[51],"Chan,":[53],"362":[57],"(2018),":[58],"346\u2013374;":[60],"T.":[61],"CSIAM":[66],"Trans.":[67],"Appl.":[68],"Math.,":[69],"1":[70],"(2020),":[71],"1\u201352]":[73],"references":[76],"therein.":[77],"However,":[78],"numerical":[81,240],"typically":[83],"generate":[84],"spurious":[85,254],"oscillations":[86,255],"in":[87,123],"presence":[89],"shock":[91],"discontinuities.":[92],"In":[93],"this":[94],"paper,":[95],"we":[96,154],"construct":[97,158],"a":[98],"stable":[102,178,236],"essentially":[103],"oscillation-free":[104],"DG":[105,179,237],"(OFDG)":[106],"method":[107,220],"for":[108,189],"laws.":[111],"With":[112],"some":[113],"suitable":[114],"modification":[115],"on":[116],"damping":[120,171,184],"term":[121,172,185],"introduced":[122],"[J.":[124],"Lu,":[125,142],"Y.":[126,139],"Liu,":[127,140],"SIAM":[131,146],"Numer.":[133],"Anal.,":[134],"59":[135],"(2021),":[136],"1299\u20131324;":[138],"Sci.":[148],"Comput.,":[149],"44":[150],"(2022),":[151],"A230\u2013A259],":[153],"able":[156],"an":[159],"OFDG":[160],"scheme":[161],"with":[162,174],"dissipative":[163,188],"entropy.":[164],"It":[165],"is":[166,202],"challenging":[167],"make":[169],"compatible":[173],"current":[176],"framework,":[180],"that":[181],"is,":[182],"should":[186],"be":[187],"any":[190],"given":[191],"function":[193,210],"without":[194],"compromising":[195],"accuracy.":[198],"The":[199],"key":[200],"ingredient":[201],"utilize":[204],"convexity":[206],"orthogonality":[213],"projection.":[216],"Then":[217],"proposed":[219,258],"maintains":[221],"same":[223],"properties":[224],"conservation,":[226],"error":[227],"estimates,":[228],"dissipation":[231],"as":[232],"original":[234],"method.":[238],"Extensive":[239],"experiments":[241],"presented":[243],"validate":[245],"theoretical":[247],"findings":[248],"capability":[251],"controlling":[253],"algorithm.Keywordshyperbolic":[259],"lawsentropy":[261],"stabilitysummation-by-partsdiscontinuous":[262],"methodnonoscillatoryMSC":[264],"codes65M1265M6076M20":[265]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
