{"id":"https://openalex.org/W2088610012","doi":"https://doi.org/10.1137/100793888","title":"A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time","display_name":"A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2088610012","doi":"https://doi.org/10.1137/100793888","mag":"2088610012"},"language":"en","primary_location":{"id":"doi:10.1137/100793888","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100793888","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/A5083733943","display_name":"Dominik Meidner","orcid":"https://orcid.org/0000-0002-4949-6356"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominik Meidner","raw_affiliation_strings":["meidner@ma.tum.de and vexler@ma.tum.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"meidner@ma.tum.de and vexler@ma.tum.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024221693","display_name":"Rolf Rannacher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rolf Rannacher","raw_affiliation_strings":["rannacher@iwr.uni-heidelberg.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"rannacher@iwr.uni-heidelberg.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085823095","display_name":"Boris Vexler","orcid":"https://orcid.org/0000-0001-6211-4263"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Boris Vexler","raw_affiliation_strings":["Heidelberg University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Heidelberg University","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4162,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.92438563,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"49","issue":"5","first_page":"1961","last_page":"1997"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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":0.9933000206947327,"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/pointwise","display_name":"Pointwise","score":0.956899881362915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8590885400772095},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7414488792419434},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7140609622001648},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7130707502365112},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6975882053375244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5043245553970337},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.48029825091362},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45107027888298035},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42668455839157104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37956005334854126},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.20154187083244324},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11611202359199524}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.956899881362915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8590885400772095},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7414488792419434},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7140609622001648},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7130707502365112},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6975882053375244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5043245553970337},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.48029825091362},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45107027888298035},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42668455839157104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37956005334854126},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.20154187083244324},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11611202359199524},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100793888","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100793888","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"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1658943","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1658943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W33773576","https://openalex.org/W1533889494","https://openalex.org/W1534416612","https://openalex.org/W1539568499","https://openalex.org/W1557358140","https://openalex.org/W1599813566","https://openalex.org/W1600371943","https://openalex.org/W1963952659","https://openalex.org/W1979080874","https://openalex.org/W2008621392","https://openalex.org/W2012560715","https://openalex.org/W2029571168","https://openalex.org/W2038626747","https://openalex.org/W2041523977","https://openalex.org/W2043841940","https://openalex.org/W2047378168","https://openalex.org/W2050357739","https://openalex.org/W2053931412","https://openalex.org/W2058731469","https://openalex.org/W2074190491","https://openalex.org/W2082621526","https://openalex.org/W2088908279","https://openalex.org/W2095630168","https://openalex.org/W2102268794","https://openalex.org/W2109168354","https://openalex.org/W2120866444","https://openalex.org/W2144865371","https://openalex.org/W2157713021","https://openalex.org/W2429258439","https://openalex.org/W2934526567","https://openalex.org/W3021722416","https://openalex.org/W3144098392","https://openalex.org/W3165030955"],"related_works":["https://openalex.org/W2034049100","https://openalex.org/W4205630301","https://openalex.org/W2119544289","https://openalex.org/W2809030115","https://openalex.org/W3165030955","https://openalex.org/W4298920371","https://openalex.org/W2949810804","https://openalex.org/W2008621392","https://openalex.org/W2107538846","https://openalex.org/W2081962455"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper,":[2],"we":[3,53],"consider":[4],"an":[5],"optimal":[6,61],"control":[7],"problem":[8],"which":[9],"is":[10,18],"governed":[11],"by":[12],"a":[13,33,48,55],"linear":[14],"parabolic":[15],"equation":[16],"and":[17],"subject":[19],"to":[20],"state":[21],"constraints":[22],"pointwise":[23],"in":[24],"time.":[25],"Optimal":[26],"order":[27],"error":[28],"estimates":[29],"are":[30],"developed":[31],"for":[32,59],"space-time":[34],"finite":[35],"element":[36],"discretization":[37],"of":[38,50],"problem.":[40],"Numerical":[41],"examples":[42],"confirm":[43],"the":[44,60],"theoretical":[45],"results.":[46],"As":[47],"by-product":[49],"our":[51],"analysis,":[52],"derive":[54],"new":[56],"regularity":[57],"result":[58],"control.":[62]},"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":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
