{"id":"https://openalex.org/W4392933172","doi":"https://doi.org/10.48550/arxiv.2403.10282","title":"Optimal Control of Stationary Doubly Diffusive Flows on Two and Three\n Dimensional Bounded Lipschitz Domains: Numerical Analysis","display_name":"Optimal Control of Stationary Doubly Diffusive Flows on Two and Three\n Dimensional Bounded Lipschitz Domains: Numerical Analysis","publication_year":2024,"publication_date":"2024-03-15","ids":{"openalex":"https://openalex.org/W4392933172","doi":"https://doi.org/10.48550/arxiv.2403.10282"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.10282","pdf_url":"http://arxiv.org/pdf/2403.10282","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2403.10282","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058616433","display_name":"Jai Tushar","orcid":"https://orcid.org/0000-0002-5773-8466"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tushar, Jai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040684079","display_name":"Arbaz Khan","orcid":"https://orcid.org/0000-0001-6625-700X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khan, Arbaz","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046452698","display_name":"Manil T. Mohan","orcid":"https://orcid.org/0000-0003-3197-1136"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohan, Manil T.","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":78},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9958,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9958,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.988,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9832,"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/lipschitz-domain","display_name":"Lipschitz domain","score":0.45490867}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8487883},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.78001714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.59670675},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.45490867},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40632492},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38575107}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.10282","pdf_url":"http://arxiv.org/pdf/2403.10282","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.10282","pdf_url":"http://arxiv.org/pdf/2403.10282","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4293385557","https://openalex.org/W4226360335","https://openalex.org/W3014335474","https://openalex.org/W2973109582","https://openalex.org/W2897842840","https://openalex.org/W2499849978","https://openalex.org/W2073281382","https://openalex.org/W2042906150","https://openalex.org/W2022300732","https://openalex.org/W1642415801"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,78],"propose":[4],"fully":[5],"nonconforming,":[6],"locally":[7],"exactly":[8],"divergence-free":[9],"discretizations":[10],"based":[11],"on":[12],"lowest":[13],"order":[14,107],"Crouziex-Raviart":[15],"finite":[16],"element":[17],"and":[18,47,55,59,96,116,141,150],"piecewise":[19],"constant":[20],"spaces":[21],"to":[22,104,156],"study":[23],"the":[24,43,80,93,113,120,123,145,152],"optimal":[25,106,126,157],"control":[26,86,94,127,158],"of":[27,42,83,122,159],"stationary":[28],"double":[29],"diffusion":[30],"model":[31],"presented":[32],"in":[33],"[B\\\"urger,":[34],"M\\'endez,":[35],"Ruiz-Baier,":[36],"SINUM":[37],"(2019),":[38],"57:1318-1343].":[39],"The":[40,125],"well-posedness":[41],"discrete":[44,53],"uncontrolled":[45],"state":[46,115],"adjoint":[48,117],"equations":[49],"are":[50,62],"discussed":[51],"using":[52,87,130],"lifting":[54],"fixed":[56],"point":[57],"arguments,":[58],"convergence":[60],"results":[61],"derived":[63],"rigorously":[64],"under":[65],"minimal":[66],"regularity.":[67],"Building":[68],"upon":[69],"our":[70],"recent":[71],"work":[72],"[Tushar,":[73],"Khan,":[74],"Mohan":[75],"arXiv":[76],"(2023)],":[77],"prove":[79,105],"local":[81],"optimality":[82,90],"a":[84,108,131,137],"reference":[85],"second-order":[88],"sufficient":[89],"condition":[91],"for":[92,112],"problem,":[95],"use":[97],"it":[98],"along":[99],"with":[100],"an":[101],"optimize-then-discretize":[102],"approach":[103],"priori":[109],"error":[110,147],"estimates":[111],"control,":[114],"variables":[118],"upto":[119],"regularity":[121],"solution.":[124],"is":[128],"computed":[129],"primal-dual":[132],"active":[133],"set":[134],"strategy":[135],"as":[136],"semi-smooth":[138],"Newton":[139],"method":[140],"computational":[142],"tests":[143],"validate":[144],"predicted":[146],"decay":[148],"rates":[149],"illustrate":[151],"proposed":[153],"scheme's":[154],"applicability":[155],"thermohaline":[160],"circulation":[161],"problems.":[162]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4392933172","counts_by_year":[],"updated_date":"2025-04-10T07:30:19.047825","created_date":"2024-03-19"}