{"id":"https://openalex.org/W2032527470","doi":"https://doi.org/10.1137/130947568","title":"On the Full and Global Accuracy of a Compact Third Order WENO Scheme","display_name":"On the Full and Global Accuracy of a Compact Third Order WENO Scheme","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2032527470","doi":"https://doi.org/10.1137/130947568","mag":"2032527470"},"language":"en","primary_location":{"id":"doi:10.1137/130947568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130947568","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/A5058869233","display_name":"Oliver Kolb","orcid":"https://orcid.org/0000-0001-6947-5520"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Oliver Kolb","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058869233"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1833,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.93612006,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"52","issue":"5","first_page":"2335","last_page":"2355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9972000122070312,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.7838871479034424},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6709489822387695},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6414879560470581},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5641903877258301},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.550389289855957},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5416879653930664},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5295337438583374},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5181840062141418},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4726765751838684},{"id":"https://openalex.org/keywords/total-variation-diminishing","display_name":"Total variation diminishing","score":0.4686533808708191},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43826204538345337},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4307776987552643},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21392083168029785}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7838871479034424},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6709489822387695},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6414879560470581},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5641903877258301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.550389289855957},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5416879653930664},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5295337438583374},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5181840062141418},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4726765751838684},{"id":"https://openalex.org/C152284280","wikidata":"https://www.wikidata.org/wiki/Q7828154","display_name":"Total variation diminishing","level":2,"score":0.4686533808708191},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43826204538345337},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4307776987552643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21392083168029785},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130947568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130947568","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"},{"id":"pmh:oai:ub-madoc.bib.uni-mannheim.de:37086","is_oa":false,"landing_page_url":"https://madoc.bib.uni-mannheim.de/37086/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196315","display_name":"MADOC (University of Mannheim)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177802217","host_organization_name":"University of Mannheim","host_organization_lineage":["https://openalex.org/I177802217"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Zeitschriftenartikel"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6800000071525574,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1969647398","https://openalex.org/W1973481688","https://openalex.org/W1975311166","https://openalex.org/W1983195644","https://openalex.org/W1987559871","https://openalex.org/W2001677793","https://openalex.org/W2020679137","https://openalex.org/W2038375355","https://openalex.org/W2038476471","https://openalex.org/W2039150507","https://openalex.org/W2044325133","https://openalex.org/W2045849310","https://openalex.org/W2048475936","https://openalex.org/W2048941652","https://openalex.org/W2054662916","https://openalex.org/W2069100091","https://openalex.org/W2083367386","https://openalex.org/W2094821511","https://openalex.org/W2097060678","https://openalex.org/W2109801076","https://openalex.org/W2122177687","https://openalex.org/W2128105245","https://openalex.org/W2158522603"],"related_works":["https://openalex.org/W2097201125","https://openalex.org/W2047079721","https://openalex.org/W2890976672","https://openalex.org/W2695482983","https://openalex.org/W1963903435","https://openalex.org/W2050140952","https://openalex.org/W2043401463","https://openalex.org/W3127074792","https://openalex.org/W2020017862","https://openalex.org/W1727763439"],"abstract_inverted_index":{"Recently,":[0],"Ar\u00e0ndiga":[1],"et":[2],"al.":[3],"showed":[4],"in":[5,27,68,143,148,177,183],"[SIAM":[6],"J.":[7,77,99],"Numer.":[8],"Anal.,":[9],"49":[10],"(2011),":[11],"pp.":[12,82,104,229],"893--915]":[13],"for":[14,110,156,207,231],"a":[15,106,214],"class":[16],"of":[17,31,41,51,92,114,122,141,180,193,195],"weighted":[18],"ENO":[19],"(WENO)":[20],"schemes":[21],"that":[22,135],"the":[23,28,32,39,42,48,60,88,111,138,144,149,174,178,181,184,190,196,208,232],"parameter":[24],"$\\varepsilon$":[25],"occurring":[26],"smoothness":[29],"indicators":[30],"scheme":[33,91,109,211,218],"should":[34],"be":[35,57],"chosen":[36],"proportional":[37],"to":[38,46,59,126],"square":[40],"mesh":[43],"size,":[44],"$h^2$,":[45],"achieve":[47,137],"optimal":[49,139],"order":[50,63,140,192,216],"accuracy.":[52],"Unfortunately,":[53],"these":[54],"results":[55,206],"cannot":[56],"applied":[58],"compact":[61],"third":[62,215],"WENO":[64,145,185,198],"reconstruction":[65,146,199],"procedure":[66,200],"introduced":[67],"[D.":[69],"Levy,":[70,97],"G.":[71,74],"Puppo,":[72],"and":[73,95,117,152,165,222],"Russo,":[75],"SIAM":[76,98],"Sci.":[78,100],"Comput.,":[79,101],"22":[80,102],"(2000),":[81,103],"656--672],":[83],"which":[84],"we":[85,132,136],"apply":[86],"within":[87],"semidiscrete":[89,210],"central":[90],"[A.":[93],"Kurganov":[94],"D.":[96],"1461--1488],":[105],"commonly":[107],"used":[108,176],"numerical":[112],"solution":[113],"conservation":[115],"laws":[116],"convection-diffusion":[118],"equations.":[119],"The":[120],"aim":[121],"this":[123,128],"paper":[124],"is":[125,173],"close":[127],"gap.":[129],"In":[130],"particular,":[131],"will":[133],"show":[134],"accuracy":[142],"($h^3$":[147],"smooth":[150],"case":[151],"$h^2$":[153],"near":[154],"discontinuities)":[155],"$\\varepsilon":[157],"=":[158],"K":[159],"h^q$":[160],"with":[161,213],"$q":[162],"\\le":[163],"3$":[164],"$pq":[166],"\\ge":[167,171],"2$,":[168],"where":[169],"$p":[170],"1$":[172],"exponent":[175],"computation":[179],"weights":[182],"scheme.":[186],"Numerical":[187],"examples":[188],"showing":[189],"predicted":[191],"convergence":[194],"analyzed":[197],"are":[201],"given":[202],"as":[203,205],"well":[204],"presented":[209],"combined":[212],"TVD--Runge--Kutta":[217],"from":[219],"[S.":[220],"Gottlieb":[221],"C.-W.":[223],"Shu,":[224],"Math.":[225],"Comp.,":[226],"67":[227],"(1998),":[228],"73--85]":[230],"time":[233],"integration.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}