{"id":"https://openalex.org/W3184678079","doi":"https://doi.org/10.1007/s10589-021-00295-2","title":"A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws","display_name":"A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws","publication_year":2021,"publication_date":"2021-07-02","ids":{"openalex":"https://openalex.org/W3184678079","doi":"https://doi.org/10.1007/s10589-021-00295-2","mag":"3184678079"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-021-00295-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00295-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00295-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00295-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016061405","display_name":"David Frenzel","orcid":null},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"David Frenzel","raw_affiliation_strings":["Department of Mathematics, Technical University of Darmstadt, Dolivostra\u00dfe 15, 64293, Darmstadt, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Darmstadt, Dolivostra\u00dfe 15, 64293, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082114163","display_name":"Jens Lang","orcid":"https://orcid.org/0000-0003-4603-6554"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jens Lang","raw_affiliation_strings":["Department of Mathematics, Technical University of Darmstadt, Dolivostra\u00dfe 15, 64293, Darmstadt, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Darmstadt, Dolivostra\u00dfe 15, 64293, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016061405"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10566017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"80","issue":"1","first_page":"301","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":1.0,"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":1.0,"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":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9986000061035156,"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/conservation-law","display_name":"Conservation law","score":0.8369603753089905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8247154951095581},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6996990442276001},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6588212251663208},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.6309576630592346},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5944335460662842},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5880274176597595},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5266242623329163},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.525439441204071},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5216313004493713},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.4579523801803589},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.44600972533226013},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37908563017845154},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.33074939250946045},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32238495349884033},{"id":"https://openalex.org/keywords/method-of-characteristics","display_name":"Method of characteristics","score":0.3000433146953583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07536867260932922}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8369603753089905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8247154951095581},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6996990442276001},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6588212251663208},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.6309576630592346},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5944335460662842},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5880274176597595},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5266242623329163},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.525439441204071},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5216313004493713},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.4579523801803589},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.44600972533226013},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37908563017845154},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.33074939250946045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32238495349884033},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.3000433146953583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07536867260932922},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10589-021-00295-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00295-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00295-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:150964","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Frenzel=3ADavid=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00295-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-021-00295-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/287360","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/287360","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10589-021-00295-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00295-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00295-2.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7099999785423279}],"awards":[{"id":"https://openalex.org/G1266455449","display_name":null,"funder_award_id":"GSC233","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1666510090","display_name":null,"funder_award_id":"TP B01","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G257168128","display_name":null,"funder_award_id":"Project-ID 239904186","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6976411281","display_name":null,"funder_award_id":"TRR154/2-2018","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323384","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3184678079.pdf","grobid_xml":"https://content.openalex.org/works/W3184678079.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1043407954","https://openalex.org/W1486816047","https://openalex.org/W1489753407","https://openalex.org/W1539037864","https://openalex.org/W1566271755","https://openalex.org/W1652296262","https://openalex.org/W1886421468","https://openalex.org/W1968156414","https://openalex.org/W1992812527","https://openalex.org/W2021601471","https://openalex.org/W2031291057","https://openalex.org/W2032119807","https://openalex.org/W2037698396","https://openalex.org/W2039150507","https://openalex.org/W2045849310","https://openalex.org/W2045873226","https://openalex.org/W2046093893","https://openalex.org/W2070533863","https://openalex.org/W2085505887","https://openalex.org/W2098101757","https://openalex.org/W2113287703","https://openalex.org/W2116729868","https://openalex.org/W2805954179","https://openalex.org/W2810105835","https://openalex.org/W2913818203","https://openalex.org/W3033042681","https://openalex.org/W3110038039","https://openalex.org/W4239495740","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2151491385","https://openalex.org/W2351702824","https://openalex.org/W2089718349","https://openalex.org/W39926494","https://openalex.org/W845104435","https://openalex.org/W2565671864","https://openalex.org/W2393704039","https://openalex.org/W2990094347","https://openalex.org/W2377182023","https://openalex.org/W144405564"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"weighted":[2],"essentially":[3],"non-oscillatory":[4],"(WENO)":[5],"methods":[6,13,22,116],"are":[7,23],"popular":[8],"and":[9,73,99,121],"effective":[10],"spatial":[11],"discretization":[12],"for":[14,54],"nonlinear":[15,62],"hyperbolic":[16,63],"partial":[17],"differential":[18],"equations.":[19],"Although":[20],"these":[21],"formally":[24],"first-order":[25,115],"accurate":[26],"when":[27],"a":[28,49,75,130],"shock":[29,42],"is":[30,67],"present,":[31],"they":[32],"still":[33],"have":[34],"uniform":[35],"high-order":[36],"accuracy":[37,132],"right":[38],"up":[39],"to":[40,60,102,113,128],"the":[41,70,84,119],"location.":[43],"In":[44],"this":[45],"paper,":[46],"we":[47],"propose":[48],"novel":[50],"third-order":[51,90],"numerical":[52],"method":[53,92,123],"solving":[55],"optimal":[56,103],"control":[57,104],"problems":[58,105],"subject":[59],"scalar":[61],"conservation":[64],"laws.":[65],"It":[66],"based":[68],"on":[69],"first-disretize-then-optimize":[71],"approach":[72],"combines":[74],"discrete":[76],"adjoint":[77],"WENO":[78],"scheme":[79],"of":[80,106],"third":[81],"order":[82],"with":[83,108,134],"classical":[85],"strong":[86],"stability":[87],"preserving":[88],"three-stage":[89],"Runge\u2013Kutta":[91],"SSPRK3.":[93],"We":[94],"analyze":[95],"its":[96,125],"approximation":[97],"properties":[98],"apply":[100],"it":[101],"tracking-type":[107],"non-smooth":[109],"target":[110],"states.":[111],"Comparisons":[112],"common":[114],"such":[117],"as":[118],"Lax\u2013Friedrichs":[120],"Engquist\u2013Osher":[122],"show":[124],"great":[126],"potential":[127],"achieve":[129],"higher":[131],"along":[133],"good":[135],"resolution":[136],"around":[137],"discontinuities.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}