{"id":"https://openalex.org/W2021072776","doi":"https://doi.org/10.1137/090759057","title":"An Entropy Adjoint Approach to Mesh Refinement","display_name":"An Entropy Adjoint Approach to Mesh Refinement","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2021072776","doi":"https://doi.org/10.1137/090759057","mag":"2021072776"},"language":"en","primary_location":{"id":"doi:10.1137/090759057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759057","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5012374585","display_name":"Krzysztof Fidkowski","orcid":"https://orcid.org/0000-0002-5106-136X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krzysztof J. Fidkowski","raw_affiliation_strings":["kfid@umich.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"kfid@umich.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074179691","display_name":"Philip L. Roe","orcid":"https://orcid.org/0000-0002-7596-2912"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philip L. Roe","raw_affiliation_strings":["philroe@umich.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"philroe@umich.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9109,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.96656891,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"32","issue":"3","first_page":"1261","last_page":"1287"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"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":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.7371397018432617},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6098405122756958},{"id":"https://openalex.org/keywords/entropy-production","display_name":"Entropy production","score":0.5655855536460876},{"id":"https://openalex.org/keywords/inviscid-flow","display_name":"Inviscid flow","score":0.5380223989486694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5282729268074036},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.4905182719230652},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48225027322769165},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.43149903416633606},{"id":"https://openalex.org/keywords/adjoint-equation","display_name":"Adjoint equation","score":0.4305829107761383},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.40735045075416565},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31828978657722473},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.25895172357559204},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.21108311414718628},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.12651649117469788},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07953110337257385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.078073650598526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7371397018432617},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6098405122756958},{"id":"https://openalex.org/C207282930","wikidata":"https://www.wikidata.org/wiki/Q5380811","display_name":"Entropy production","level":2,"score":0.5655855536460876},{"id":"https://openalex.org/C86252789","wikidata":"https://www.wikidata.org/wiki/Q2247765","display_name":"Inviscid flow","level":2,"score":0.5380223989486694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5282729268074036},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.4905182719230652},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48225027322769165},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.43149903416633606},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.4305829107761383},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.40735045075416565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31828978657722473},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25895172357559204},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.21108311414718628},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12651649117469788},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07953110337257385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.078073650598526},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090759057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759057","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W606836880","https://openalex.org/W1678237772","https://openalex.org/W1981885012","https://openalex.org/W1986997550","https://openalex.org/W1989864369","https://openalex.org/W1992833209","https://openalex.org/W2006272017","https://openalex.org/W2011252206","https://openalex.org/W2012193172","https://openalex.org/W2027619967","https://openalex.org/W2032966402","https://openalex.org/W2050051055","https://openalex.org/W2052385123","https://openalex.org/W2060951497","https://openalex.org/W2106476375","https://openalex.org/W2106693264","https://openalex.org/W2110781362","https://openalex.org/W2113619058","https://openalex.org/W2122177687","https://openalex.org/W2133147107","https://openalex.org/W2138746820","https://openalex.org/W2159995532","https://openalex.org/W2165187821","https://openalex.org/W2165804517","https://openalex.org/W4233241017"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W1486213812","https://openalex.org/W2044987316","https://openalex.org/W3134374554","https://openalex.org/W2237480245","https://openalex.org/W2877193653","https://openalex.org/W327736757","https://openalex.org/W2965825062"],"abstract_inverted_index":{"This":[0],"work":[1,34],"presents":[2],"a":[3,44],"mesh":[4],"refinement":[5],"indicator":[6],"based":[7],"on":[8,91,129],"entropy":[9,20,63,76,84,97,111],"variables,":[10,85],"with":[11,54,131,144],"an":[12,26,29],"application":[13],"to":[14,24,39,60,89,157],"the":[15,55,62,66,80,92,96,104,145,149],"compressible":[16],"Navier\u2013Stokes":[17],"equations.":[18],"The":[19,51],"variables":[21],"are":[22],"shown":[23,59],"satisfy":[25],"adjoint":[27,57,154],"equation,":[28,99],"observation":[30],"that":[31,152],"allows":[32],"recent":[33],"in":[35,42,65,121,138],"adjoint-based":[36],"error":[37],"estimation":[38],"be":[40,61,158],"leveraged":[41],"constructing":[43],"relatively":[45],"cheap":[46],"but":[47],"effective":[48],"adaptive":[49],"indicator.":[50],"output":[52],"associated":[53],"entropy-variable":[56],"is":[58,87],"production":[64],"computational":[67],"domain,":[68],"including":[69],"physical":[70],"viscous":[71,118],"dissipation":[72],"when":[73],"present,":[74],"minus":[75],"transport":[77,98],"out":[78],"of":[79,95,103,142,148],"domain.":[81],"Adaptation":[82],"using":[83],"which":[86],"equivalent":[88],"adapting":[90],"integrated":[93],"residual":[94],"thus":[100],"targets":[101],"areas":[102],"domain":[105],"responsible":[106],"for":[107,115],"numerical,":[108],"or":[109],"spurious,":[110],"production.":[112],"Adaptive":[113],"results":[114],"inviscid":[116],"and":[117,123],"aerodynamic":[119],"examples":[120],"two":[122],"three":[124],"dimensions":[125],"demonstrate":[126],"performance":[127],"efficiency":[128],"par":[130],"output-based":[132],"adaptation,":[133],"as":[134],"measured":[135],"by":[136],"errors":[137],"various":[139],"engineering":[140],"quantities":[141],"interest,":[143],"comparative":[146],"advantage":[147],"proposed":[150],"approach":[151],"no":[153],"equations":[155],"need":[156],"solved.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}