{"id":"https://openalex.org/W4403247869","doi":"https://doi.org/10.1090/mcom/4037","title":"Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge\u2013Kutta discontinuous Galerkin method","display_name":"Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge\u2013Kutta discontinuous Galerkin method","publication_year":2024,"publication_date":"2024-10-09","ids":{"openalex":"https://openalex.org/W4403247869","doi":"https://doi.org/10.1090/mcom/4037"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4037","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4037","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5000504797","display_name":"Zheng Sun","orcid":"https://orcid.org/0000-0003-3763-3015"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zheng Sun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000504797"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5483,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66644499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"94","issue":"356","first_page":"2795","last_page":"2838"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.9954000115394592,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.8002632260322571},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7899506688117981},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6856033802032471},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.6536144018173218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6248664259910583},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.6188037991523743},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5779853463172913},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5748332738876343},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5221657752990723},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4743313193321228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4356018602848053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1607239842414856},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.15149253606796265},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14516031742095947},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10911908745765686},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09282347559928894}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8002632260322571},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7899506688117981},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6856033802032471},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.6536144018173218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6248664259910583},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.6188037991523743},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5779853463172913},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5748332738876343},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5221657752990723},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4743313193321228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4356018602848053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1607239842414856},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.15149253606796265},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14516031742095947},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10911908745765686},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09282347559928894},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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:10.1090/mcom/4037","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4037","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1287316037","display_name":"Institute for Computational and Experimental Research in Mathematics","funder_award_id":"1929284","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1409578402","display_name":"Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Systems with Compact Stencils","funder_award_id":"2208391","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1486816047","https://openalex.org/W1507767947","https://openalex.org/W1791091458","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/W2014282047","https://openalex.org/W2022818818","https://openalex.org/W2065908448","https://openalex.org/W2081377160","https://openalex.org/W2085961649","https://openalex.org/W2092436849","https://openalex.org/W2116729868","https://openalex.org/W2125822172","https://openalex.org/W2130350269","https://openalex.org/W2463552244","https://openalex.org/W2507558872","https://openalex.org/W2581973763","https://openalex.org/W2587498379","https://openalex.org/W2743040688","https://openalex.org/W2765460213","https://openalex.org/W2902420577","https://openalex.org/W2945076242","https://openalex.org/W2956097844","https://openalex.org/W2990682730","https://openalex.org/W3011239099","https://openalex.org/W3042250044","https://openalex.org/W3093401606","https://openalex.org/W3116961995","https://openalex.org/W3179588297","https://openalex.org/W3204708751","https://openalex.org/W4214751139","https://openalex.org/W4221156852","https://openalex.org/W4225731490","https://openalex.org/W4238285603","https://openalex.org/W4246409132","https://openalex.org/W4252060206","https://openalex.org/W4285362429","https://openalex.org/W4285394736","https://openalex.org/W4327694453","https://openalex.org/W4384389921","https://openalex.org/W4390058406","https://openalex.org/W4394761857","https://openalex.org/W4398156712","https://openalex.org/W4400610270"],"related_works":["https://openalex.org/W2167521757","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2885311694","https://openalex.org/W2013813162","https://openalex.org/W2887215440","https://openalex.org/W2963636343","https://openalex.org/W3102618207","https://openalex.org/W3098143598","https://openalex.org/W1964985536"],"abstract_inverted_index":{"The":[0,166],"Runge\u2013Kutta":[1],"(RK)":[2],"discontinuous":[3],"Galerkin":[4],"(DG)":[5],"method":[6,140,168,182],"is":[7,173],"a":[8,31,174],"mainstream":[9],"numerical":[10,139,167],"algorithm":[11],"for":[12,128,202,213],"solving":[13],"hyperbolic":[14],"equations.":[15],"In":[16],"this":[17,171],"paper,":[18],"we":[19,51,79],"use":[20,52,98],"the":[21,36,53,74,81,99,129,137,143,154,164,178,227],"linear":[22],"advection":[23],"equation":[24],"in":[25,45,73,170],"one":[26],"and":[27,97,148,191,205,223],"two":[28],"dimensions":[29],"as":[30,48,50,151],"model":[32],"problem":[33],"to":[34,162],"prove":[35],"following":[37],"results:":[38],"For":[39],"an":[40],"arbitrarily":[41],"high-order":[42],"RKDG":[43,156,181],"scheme":[44],"Butcher":[46],"form,":[47],"long":[49],"<inline-formula":[54,82,100],"content-type=\"math/mathml\">":[55,83,101],"<mml:math":[56,84,102],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[57,85,103],"alttext=\"upper":[58,104],"P":[59,105],"Superscript":[60,106],"k\">":[61],"<mml:semantics>":[62,87,110],"<mml:msup>":[63,111],"<mml:mi>P</mml:mi>":[64,112],"<mml:mi>k</mml:mi>":[65,88,115],"</mml:msup>":[66,121],"<mml:annotation":[67,89,122],"encoding=\"application/x-tex\">P^k</mml:annotation>":[68],"</mml:semantics>":[69,91,124],"</mml:math>":[70,92,125],"</inline-formula>":[71,93,126],"approximation":[72,127],"final":[75],"stage,":[76],"even":[77],"if":[78],"drop":[80],"alttext=\"k\">":[86],"encoding=\"application/x-tex\">k</mml:annotation>":[90],"th-order":[94],"polynomial":[95,185],"modes":[96],"k":[107],"minus":[108],"1\">":[109],"<mml:mrow":[113],"class=\"MJX-TeXAtom-ORD\">":[114],"<mml:mo>":[116],"\u2212":[117],"</mml:mo>":[118],"<mml:mn>1</mml:mn>":[119],"</mml:mrow>":[120],"encoding=\"application/x-tex\">P^{k-1}</mml:annotation>":[123],"DG":[130,217],"operators":[131],"at":[132,209],"all":[133],"inner":[134],"RK":[135,211],"stages,":[136],"resulting":[138],"still":[141],"maintains":[142],"same":[144],"type":[145,222],"of":[146,153,177,226],"stability":[147,221],"convergence":[149],"rate":[150],"those":[152],"original":[155,228],"method.":[157,229],"Numerical":[158],"examples":[159],"are":[160],"provided":[161],"validate":[163],"analysis.":[165],"analyzed":[169],"paper":[172],"special":[175],"case":[176],"Class":[179],"A":[180],"with":[183],"stage-dependent":[184],"spaces":[186],"proposed":[187],"by":[188],"Chen,":[189],"Sun,":[190],"Xing":[192],"[arXiv":[193],"preprint,":[194],"arXiv:2402.15150,":[195],"2024].":[196],"Our":[197],"analysis":[198],"provides":[199],"theoretical":[200],"justifications":[201],"employing":[203],"cost-effective":[204],"low-order":[206],"spatial":[207],"discretization":[208],"specific":[210],"stages":[212],"developing":[214],"more":[215],"efficient":[216],"schemes":[218],"without":[219],"affecting":[220],"accuracy":[224],"order":[225]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2024-10-10T00:00:00"}