{"id":"https://openalex.org/W4395030531","doi":"https://doi.org/10.1515/cmam-2023-0171","title":"A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control","display_name":"A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control","publication_year":2024,"publication_date":"2024-04-23","ids":{"openalex":"https://openalex.org/W4395030531","doi":"https://doi.org/10.1515/cmam-2023-0171"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2023-0171","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0171","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/310873","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049432379","display_name":"Fabio Zoccolan","orcid":"https://orcid.org/0000-0002-5845-8415"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Fabio Zoccolan","raw_affiliation_strings":["Institute of Mathematics , 27218 \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , 1015 Lausanne , Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , 27218 \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , 1015 Lausanne , Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085926069","display_name":"Maria Strazzullo","orcid":"https://orcid.org/0000-0003-1245-271X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Strazzullo","raw_affiliation_strings":["Department of Mathematical Sciences \u201dGiuseppe Luigi Lagrange\u201d , 19032 Politecnico di Torino , Corso Duca degli Abruzzi 24, 10129 , Turin , Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences \u201dGiuseppe Luigi Lagrange\u201d , 19032 Politecnico di Torino , Corso Duca degli Abruzzi 24, 10129 , Turin , Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061558433","display_name":"Gianluigi Rozza","orcid":"https://orcid.org/0000-0002-0810-8812"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Gianluigi Rozza","raw_affiliation_strings":["mathLab , Mathematics Area , 19040 SISSA , via Bonomea 265, 34136 Trieste , Italy"],"affiliations":[{"raw_affiliation_string":"mathLab , Mathematics Area , 19040 SISSA , via Bonomea 265, 34136 Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061558433"],"corresponding_institution_ids":["https://openalex.org/I138549579"],"apc_list":null,"apc_paid":null,"fwci":1.9688,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8561295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"25","issue":"1","first_page":"237","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9993000030517578,"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":0.9987000226974487,"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/discretization","display_name":"Discretization","score":0.7879908084869385},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.7653744220733643},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.626301646232605},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6035957336425781},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5946687459945679},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5934622287750244},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5108663439750671},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5092057585716248},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.5087223649024963},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.489096462726593},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4600323438644409},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.45665207505226135},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.43772539496421814},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36848336458206177},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31287044286727905},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09930115938186646}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7879908084869385},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.7653744220733643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.626301646232605},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6035957336425781},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5946687459945679},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5934622287750244},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5108663439750671},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5092057585716248},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.5087223649024963},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.489096462726593},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4600323438644409},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.45665207505226135},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.43772539496421814},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36848336458206177},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31287044286727905},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09930115938186646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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":2,"locations":[{"id":"doi:10.1515/cmam-2023-0171","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0171","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:310873","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/310873","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:310873","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/310873","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1554696454","https://openalex.org/W1592302811","https://openalex.org/W1964507860","https://openalex.org/W1978399516","https://openalex.org/W2005586154","https://openalex.org/W2010619938","https://openalex.org/W2012386000","https://openalex.org/W2020060524","https://openalex.org/W2024923766","https://openalex.org/W2047338836","https://openalex.org/W2050428953","https://openalex.org/W2052690618","https://openalex.org/W2070299075","https://openalex.org/W2073897969","https://openalex.org/W2093049475","https://openalex.org/W2095060406","https://openalex.org/W2096408840","https://openalex.org/W2110770808","https://openalex.org/W2115291951","https://openalex.org/W2116621195","https://openalex.org/W2124056301","https://openalex.org/W2128702576","https://openalex.org/W2131712881","https://openalex.org/W2133041109","https://openalex.org/W2139953411","https://openalex.org/W2140820418","https://openalex.org/W2148294545","https://openalex.org/W2506719423","https://openalex.org/W2607498875","https://openalex.org/W2752626032","https://openalex.org/W2753365189","https://openalex.org/W2772817569","https://openalex.org/W2895139727","https://openalex.org/W2963340469","https://openalex.org/W3033721662","https://openalex.org/W3102097232","https://openalex.org/W3210728045","https://openalex.org/W3211378307","https://openalex.org/W4206565284","https://openalex.org/W4240395309","https://openalex.org/W4245654886","https://openalex.org/W4292079189","https://openalex.org/W4294836170","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W3028496900","https://openalex.org/W2292433181","https://openalex.org/W2063214641","https://openalex.org/W2353574330","https://openalex.org/W4395030531","https://openalex.org/W1977653078","https://openalex.org/W1996072987","https://openalex.org/W827405462","https://openalex.org/W1980517550","https://openalex.org/W1972136974"],"abstract_inverted_index":{"Abstract":[0],"In":[1,23,115],"this":[2,24,94,156],"paper":[3],"we":[4,87,128],"will":[5,52,71,76,88,129],"consider":[6,130],"distributed":[7],"Linear-Quadratic":[8],"Optimal":[9],"Control":[10],"Problems":[11],"dealing":[12],"with":[13,177],"Advection-Diffusion":[14],"PDEs":[15],"for":[16,30,122],"high":[17],"values":[18],"of":[19],"the":[20,43,64,111,119,142,169,178],"P\u00e9clet":[21],"number.":[22],"situation,":[25],"computational":[26,163,180],"instabilities":[27],"occur,":[28],"both":[29,80],"steady":[31],"and":[32,74,97,125,171],"unsteady":[33],"cases.":[34],"A":[35],"Streamline":[36],"Upwind":[37],"Petrov\u2013Galerkin":[38],"technique":[39],"is":[40,108,141,160],"used":[41],"in":[42,59,79,110,136,155],"optimality":[44],"system":[45],"to":[46,117,151],"overcome":[47],"these":[48],"unpleasant":[49],"effects.":[50],"We":[51],"apply":[53],"a":[54,67,131,137],"finite":[55],"element":[56],"method":[57],"discretization":[58,95],"an":[60],"optimize-then-discretize":[61],"approach.":[62,139],"Concerning":[63],"parabolic":[65,153],"case,":[66],"stabilized":[68,152],"space-time":[69],"framework":[70],"be":[72,102],"considered":[73],"stabilization":[75,107],"also":[77],"occur":[78],"bilinear":[81],"forms":[82],"involving":[83],"time":[84,144],"derivatives.":[85],"Then":[86],"build":[89,118],"Reduced":[90,146],"Order":[91,147],"Models":[92,148],"on":[93],"procedure":[96],"two":[98],"possible":[99],"settings":[100],"can":[101],"analyzed:":[103],"whether":[104],"or":[105],"not":[106],"needed":[109],"online":[112],"phase,":[113],"too.":[114],"order":[116],"reduced":[120],"bases":[121],"state,":[123],"control,":[124],"adjoint":[126],"variables":[127],"Proper":[132],"Orthogonal":[133],"Decomposition":[134],"algorithm":[135],"partitioned":[138],"It":[140],"first":[143],"that":[145],"are":[149,174],"applied":[150],"problems":[154],"setting.":[157],"The":[158],"discussion":[159],"supported":[161],"by":[162],"experiments,":[164],"where":[165],"relative":[166],"errors":[167],"between":[168],"FEM":[170],"ROM":[172],"solutions":[173],"studied":[175],"together":[176],"respective":[179],"times.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2024-04-24T00:00:00"}
