{"id":"https://openalex.org/W2081377160","doi":"https://doi.org/10.1137/090771363","title":"Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge\u2013Kutta Discontinuous Galerkin Method for Scalar Conservation Laws","display_name":"Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge\u2013Kutta Discontinuous Galerkin Method for Scalar Conservation Laws","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2081377160","doi":"https://doi.org/10.1137/090771363","mag":"2081377160"},"language":"en","primary_location":{"id":"doi:10.1137/090771363","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771363","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5027410721","display_name":"Qiang Zhang","orcid":"https://orcid.org/0000-0003-1796-7042"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qiang Zhang","raw_affiliation_strings":["qzh@nju.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"qzh@nju.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":["shu@dam.brown.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"shu@dam.brown.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027410721"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8642,"has_fulltext":false,"cited_by_count":153,"citation_normalized_percentile":{"value":0.97438383,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"48","issue":"3","first_page":"1038","last_page":"1063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8709829449653625},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.8499829769134521},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7344841957092285},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.7065274715423584},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7065033912658691},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6782484650611877},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6626367568969727},{"id":"https://openalex.org/keywords/courant\u2013friedrichs\u2013lewy-condition","display_name":"Courant\u2013Friedrichs\u2013Lewy condition","score":0.5805115699768066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5616832375526428},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.507951557636261},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5074254870414734},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4757349491119385},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.467131644487381},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4650987386703491},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4042079448699951},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3114561140537262},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.2910798490047455},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16029903292655945},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0941067636013031}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8709829449653625},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8499829769134521},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7344841957092285},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.7065274715423584},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7065033912658691},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6782484650611877},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6626367568969727},{"id":"https://openalex.org/C30295242","wikidata":"https://www.wikidata.org/wiki/Q1023483","display_name":"Courant\u2013Friedrichs\u2013Lewy condition","level":3,"score":0.5805115699768066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5616832375526428},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.507951557636261},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5074254870414734},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4757349491119385},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.467131644487381},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4650987386703491},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4042079448699951},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3114561140537262},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.2910798490047455},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16029903292655945},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0941067636013031},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090771363","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771363","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W175182215","https://openalex.org/W202835528","https://openalex.org/W1507767947","https://openalex.org/W1967575591","https://openalex.org/W1973481688","https://openalex.org/W1982465309","https://openalex.org/W1982883068","https://openalex.org/W1987826592","https://openalex.org/W1993923624","https://openalex.org/W1994099903","https://openalex.org/W1996082552","https://openalex.org/W2003438645","https://openalex.org/W2006015046","https://openalex.org/W2012938047","https://openalex.org/W2022818818","https://openalex.org/W2065908448","https://openalex.org/W2082388745","https://openalex.org/W2085961649","https://openalex.org/W2092891737","https://openalex.org/W3010292040","https://openalex.org/W4236438452","https://openalex.org/W4245820193","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W1964985536","https://openalex.org/W3158094109","https://openalex.org/W1965314915","https://openalex.org/W2006321195","https://openalex.org/W3173954856","https://openalex.org/W4287752683","https://openalex.org/W1994099903","https://openalex.org/W1996082552","https://openalex.org/W2081377160","https://openalex.org/W2010894337"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"an":[5,34],"analysis":[6],"of":[7,57,117],"the":[8,19,23,39,91,103,111],"Runge\u2013Kutta":[9,30],"discontinuous":[10],"Galerkin":[11],"method":[12],"for":[13,42,54,66,75,83],"solving":[14],"scalar":[15,43,58],"conservation":[16,45,60],"laws,":[17],"where":[18,98],"time":[20,107],"discretization":[21],"is":[22,64,73,115],"third":[24],"order":[25,63,72],"explicit":[26],"total":[27],"variation":[28],"diminishing":[29],"method.":[31],"We":[32],"use":[33],"energy":[35],"technique":[36],"to":[37,48],"prove":[38],"$\\mathrm{L}^2$-norm":[40],"stability":[41],"linear":[44],"laws":[46],"and":[47,70,100,106,110,119],"obtain":[49],"a":[50],"priori":[51],"error":[52],"estimates":[53],"smooth":[55],"solutions":[56],"nonlinear":[59],"laws.":[61],"Quasi-optimal":[62],"obtained":[65,82],"general":[67],"numerical":[68],"fluxes,":[69],"optimal":[71],"given":[74],"upwind":[76],"fluxes.":[77],"The":[78],"theoretical":[79],"results":[80],"are":[81,102],"piecewise":[84],"polynomials":[85],"with":[86],"any":[87],"degree":[88],"$k\\geq1$":[89],"under":[90],"standard":[92],"temporal-spatial":[93],"CFL":[94],"condition":[95],"$\\tau\\leq\\gamma":[96],"h$,":[97],"h":[99,118],"$\\tau$":[101],"element":[104],"length":[105],"step,":[108],"respectively,":[109],"positive":[112],"constant":[113],"$\\gamma$":[114],"independent":[116],"$\\tau$.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}