{"id":"https://openalex.org/W4311802675","doi":"https://doi.org/10.1137/21m145361x","title":"Finite Element Analysis of a Constrained Dirichlet Boundary Control Problem Governed by a Linear Parabolic Equation","display_name":"Finite Element Analysis of a Constrained Dirichlet Boundary Control Problem Governed by a Linear Parabolic Equation","publication_year":2022,"publication_date":"2022-12-15","ids":{"openalex":"https://openalex.org/W4311802675","doi":"https://doi.org/10.1137/21m145361x"},"language":"en","primary_location":{"id":"doi:10.1137/21m145361x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m145361x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5014633098","display_name":"Thirupathi Gudi","orcid":"https://orcid.org/0000-0003-2093-1382"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Thirupathi Gudi","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031005588","display_name":"Gouranga Mallik","orcid":"https://orcid.org/0000-0002-8719-8376"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gouranga Mallik","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India"],"raw_orcid":"https://orcid.org/0000-0002-8719-8376","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087008012","display_name":"Ramesh Ch. Sau","orcid":"https://orcid.org/0000-0001-7558-7967"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramesh Ch. Sau","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India"],"raw_orcid":"https://orcid.org/0000-0001-7558-7967","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.4762,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56518422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"60","issue":"6","first_page":"3262","last_page":"3288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983000159263611,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8950377702713013},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6933318376541138},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6466495990753174},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5731929540634155},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5601100325584412},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5550004839897156},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5265969038009644},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5047811269760132},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4757232964038849},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.46595698595046997},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4496203660964966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4372377097606659},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4187270998954773},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4136575758457184},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2510886788368225}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8950377702713013},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6933318376541138},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6466495990753174},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5731929540634155},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5601100325584412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5550004839897156},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5265969038009644},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5047811269760132},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4757232964038849},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.46595698595046997},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4496203660964966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4372377097606659},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4187270998954773},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4136575758457184},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2510886788368225},{"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":1,"locations":[{"id":"doi:10.1137/21m145361x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m145361x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2558722071","display_name":null,"funder_award_id":"R(IA)/CVR-PDF/2020","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W126240089","https://openalex.org/W616225202","https://openalex.org/W1532600003","https://openalex.org/W1536279384","https://openalex.org/W1601728065","https://openalex.org/W1820125862","https://openalex.org/W1855169650","https://openalex.org/W1926947049","https://openalex.org/W1971226930","https://openalex.org/W1981159109","https://openalex.org/W1981611107","https://openalex.org/W1984479582","https://openalex.org/W1990941154","https://openalex.org/W1992893649","https://openalex.org/W2008621392","https://openalex.org/W2009985306","https://openalex.org/W2010207646","https://openalex.org/W2019614926","https://openalex.org/W2023776730","https://openalex.org/W2031821805","https://openalex.org/W2041304886","https://openalex.org/W2041983444","https://openalex.org/W2062618977","https://openalex.org/W2132729901","https://openalex.org/W2251490743","https://openalex.org/W2461866128","https://openalex.org/W2908196854","https://openalex.org/W2994939066","https://openalex.org/W3165030955","https://openalex.org/W4248903561","https://openalex.org/W4300184951"],"related_works":["https://openalex.org/W2123186262","https://openalex.org/W1605598954","https://openalex.org/W2086063693","https://openalex.org/W2088607708","https://openalex.org/W4391019786","https://openalex.org/W184885699","https://openalex.org/W2623925491","https://openalex.org/W2131114525","https://openalex.org/W1967450583","https://openalex.org/W4319323459"],"abstract_inverted_index":{"This":[0],"article":[1],"considers":[2],"finite":[3,93,115],"element":[4],"analysis":[5],"of":[6,29,38,53,85,122,124],"a":[7,24,54,74],"Dirichlet":[8,19],"boundary":[9],"control":[10,20,60,80,108],"problem":[11,61,77],"governed":[12],"by":[13,145],"the":[14,30,36,39,51,58,64,79,86,96,107,111,127,138],"linear":[15],"parabolic":[16,40],"equation.":[17],"The":[18,67,82,140],"is":[21,89,99],"considered":[22],"in":[23,73,126],"closed":[25],"and":[26,44,62,130],"convex":[27],"subset":[28],"energy":[31],"space":[32,83],".":[33],"We":[34,49,117],"discuss":[35],"well-posedness":[37],"partial":[41],"differential":[42],"equation":[43],"derive":[45,63,118],"some":[46,134,146],"stability":[47],"estimates.":[48],"prove":[50],"existence":[52],"unique":[55],"solution":[56],"to":[57],"optimal":[59,120],"optimality":[65,70],"system.":[66],"first-order":[68],"necessary":[69],"condition":[71],"results":[72,142],"simplified":[75],"Signorini-type":[76],"for":[78],"variable.":[81],"discretization":[84,98],"state":[87,132],"variable":[88],"done":[90],"using":[91],"conforming":[92,112],"elements,":[94],"whereas":[95],"time":[97],"based":[100],"on":[101,137],"discontinuous":[102],"Galerkin":[103],"methods.":[104],"To":[105],"discretize":[106],"we":[109],"use":[110],"prismatic":[113],"Lagrange":[114],"elements.":[116],"an":[119],"order":[121],"convergence":[123],"error":[125],"control,":[128],"state,":[129],"adjoint":[131],"under":[133],"regularity":[135],"assumptions":[136],"solutions.":[139],"theoretical":[141],"are":[143],"corroborated":[144],"numerical":[147],"tests.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-12-28T00:00:00"}
