{"id":"https://openalex.org/W1996082552","doi":"https://doi.org/10.1137/040620382","title":"Error Estimates to Smooth Solutions of Runge\u2013Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws","display_name":"Error Estimates to Smooth Solutions of Runge\u2013Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1996082552","doi":"https://doi.org/10.1137/040620382","mag":"1996082552"},"language":"en","primary_location":{"id":"doi:10.1137/040620382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620382","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/A5100381999","display_name":"Qiang Zhang","orcid":"https://orcid.org/0000-0003-3776-9799"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qiang Zhang","raw_affiliation_strings":[],"affiliations":[]},{"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\u2010Wang Shu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100381999"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2341,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.7821013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"1703","last_page":"1720"},"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":0.9994999766349792,"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":0.9973000288009644,"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":0.8866008520126343},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8031562566757202},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8012211322784424},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7505661249160767},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6984242796897888},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6847119927406311},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5803102254867554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5735899806022644},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5546725988388062},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5519424080848694},{"id":"https://openalex.org/keywords/courant\u2013friedrichs\u2013lewy-condition","display_name":"Courant\u2013Friedrichs\u2013Lewy condition","score":0.4617566764354706},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4304197132587433},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4105866551399231},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3276987671852112},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07453510165214539}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8866008520126343},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8031562566757202},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8012211322784424},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7505661249160767},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6984242796897888},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6847119927406311},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5803102254867554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5735899806022644},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5546725988388062},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5519424080848694},{"id":"https://openalex.org/C30295242","wikidata":"https://www.wikidata.org/wiki/Q1023483","display_name":"Courant\u2013Friedrichs\u2013Lewy condition","level":3,"score":0.4617566764354706},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4304197132587433},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4105866551399231},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3276987671852112},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07453510165214539},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040620382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620382","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":[{"id":"https://metadata.un.org/sdg/15","score":0.7300000190734863,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W175182215","https://openalex.org/W202835528","https://openalex.org/W1507767947","https://openalex.org/W1555627060","https://openalex.org/W1658069724","https://openalex.org/W1967575591","https://openalex.org/W1973481688","https://openalex.org/W1982465309","https://openalex.org/W1982883068","https://openalex.org/W1990142375","https://openalex.org/W1993923624","https://openalex.org/W1994099903","https://openalex.org/W1997654684","https://openalex.org/W1998602489","https://openalex.org/W1998830482","https://openalex.org/W2008179816","https://openalex.org/W2012938047","https://openalex.org/W2065908448","https://openalex.org/W2068056613","https://openalex.org/W2070217589","https://openalex.org/W2085961649","https://openalex.org/W2092436849","https://openalex.org/W2092891737","https://openalex.org/W3010292040","https://openalex.org/W4245037559","https://openalex.org/W4245820193","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W2726528067","https://openalex.org/W2129573473","https://openalex.org/W2380255313","https://openalex.org/W2952149072","https://openalex.org/W2154700905","https://openalex.org/W1964985536","https://openalex.org/W2092808148","https://openalex.org/W2071331898","https://openalex.org/W1977737476","https://openalex.org/W1841315488"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"the":[5,19,28,38,52,58,82,88],"error":[6,53],"estimates":[7,103],"to":[8],"sufficiently":[9],"smooth":[10],"solutions":[11],"of":[12,15,98],"symmetrizable":[13],"systems":[14,67,74],"conservation":[16],"laws":[17],"for":[18,65,72,104],"Runge\u2013Kutta":[20,35],"discontinuous":[21],"Galerkin":[22],"(RKDG)":[23],"method.":[24],"Time":[25],"discretization":[26],"is":[27,44,55,81,87,93],"second\u2010order":[29],"explicit":[30],"TVD":[31],"(total":[32],"variation":[33],"diminishing)":[34],"method,":[36],"and":[37,71,91,100],"$\\mathbb{P}^k$":[39,105],"(piecewise":[40,48],"polynomial)":[41],"finite":[42,50,106],"element":[43,84],"used.":[45],"When":[46],"$k=1$":[47],"linear":[49,73],"element),":[51],"estimate":[54],"obtained":[56,111],"under":[57,112],"usual":[59],"CFL":[60,116],"condition":[61],"$\\dt\\leq":[62],"\\beta":[63],"h$":[64],"nonlinear":[66],"in":[68,75],"one":[69],"dimension":[70],"multiple":[76],"space":[77],"dimensions.":[78],"Here,":[79],"h":[80,99],"maximum":[83],"length,":[85],"\u03c4":[86],"time":[89],"step,":[90],"\u03b2":[92],"a":[94,113],"positive":[95],"constant":[96],"independent":[97],"\u03c4.":[101],"Error":[102],"elements":[107],"with":[108],"$k>1$":[109],"are":[110],"more":[114],"restrictive":[115],"condition.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
