{"id":"https://openalex.org/W2591235185","doi":"https://doi.org/10.1137/17m1117768","title":"The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences","display_name":"The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2591235185","doi":"https://doi.org/10.1137/17m1117768","mag":"2591235185"},"language":"en","primary_location":{"id":"doi:10.1137/17m1117768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1117768","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1608.01726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"J\u00e9rome Droniou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00e9rome Droniou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Neela Nataraj","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neela Nataraj","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Devika Shylaja","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Devika Shylaja","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.741,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67740047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"55","issue":"6","first_page":"3640","last_page":"3672"},"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":0.755299985408783,"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":0.755299985408783,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.04859999939799309,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.028999999165534973,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.9581000208854675},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7558000087738037},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7294999957084656},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6485999822616577},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4846999943256378},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.47589999437332153},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.44909998774528503},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.43549999594688416}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9581000208854675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8794999718666077},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7558000087738037},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7294999957084656},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6485999822616577},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5454999804496765},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4846999943256378},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44339999556541443},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4296000003814697},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.41200000047683716},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.35830000042915344},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1117768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1117768","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:arXiv.org:1608.01726","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1608.01726","pdf_url":"https://arxiv.org/pdf/1608.01726","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1608.01726","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1608.01726","pdf_url":"https://arxiv.org/pdf/1608.01726","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3349725324","display_name":null,"funder_award_id":"SR/S4/MS","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4527158812","display_name":null,"funder_award_id":"SR/S4/MS/808/12","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G5125659480","display_name":null,"funder_award_id":"DP170100605","funder_id":"https://openalex.org/F4320315885","funder_display_name":"Australian Government"}],"funders":[{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"},{"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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2591235185.pdf","grobid_xml":"https://content.openalex.org/works/W2591235185.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1257148767","https://openalex.org/W1821352674","https://openalex.org/W1935825599","https://openalex.org/W1968754888","https://openalex.org/W2021370156","https://openalex.org/W2024466759","https://openalex.org/W2031821805","https://openalex.org/W2034201182","https://openalex.org/W2043994920","https://openalex.org/W2045526409","https://openalex.org/W2053085169","https://openalex.org/W2058059020","https://openalex.org/W2061861714","https://openalex.org/W2064124082","https://openalex.org/W2074783170","https://openalex.org/W2084188495","https://openalex.org/W2097964994","https://openalex.org/W2126086928","https://openalex.org/W2129060539","https://openalex.org/W2130763970","https://openalex.org/W2145302287","https://openalex.org/W2154745957","https://openalex.org/W2283775600","https://openalex.org/W2597248869","https://openalex.org/W4293032004","https://openalex.org/W4297968680"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"optimal":[3],"control":[4,36,44],"problems":[5],"governed":[6],"by":[7],"diffusion":[8],"equations":[9],"with":[10],"Dirichlet":[11],"and":[12,43,75,92],"Neumann":[13],"boundary":[14],"conditions":[15],"are":[16,28,46,61,66,86],"investigated":[17],"in":[18],"the":[19,22,31,35,58,77,89],"framework":[20],"of":[21,34,83],"gradient":[23,51],"discretization":[24],"method.":[25],"Gradient":[26],"schemes":[27,52],"defined":[29],"for":[30,40,50,88],"optimality":[32],"system":[33],"problem.":[37],"Error":[38],"estimates":[39],"state,":[41],"adjoint,":[42],"variables":[45],"derived.":[47],"Superconvergence":[48],"results":[49,65],"under":[53],"realistic":[54],"regularity":[55],"assumptions":[56],"on":[57],"exact":[59],"solution":[60],"discussed.":[62],"These":[63],"superconvergence":[64],"shown":[67],"to":[68,70,76],"apply":[69],"nonconforming":[71,91],"$\\mathbb{P}_1$":[72],"finite":[73,80,95],"elements":[74],"mixed-hybrid":[78,93],"mimetic":[79,94],"differences.":[81],"Results":[82],"numerical":[84],"experiments":[85],"demonstrated":[87],"conforming,":[90],"difference":[96],"schemes.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-03-03T00:00:00"}
