{"id":"https://openalex.org/W2613481459","doi":"https://doi.org/10.1515/cmam-2017-0054","title":"Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method","display_name":"Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method","publication_year":2017,"publication_date":"2017-12-05","ids":{"openalex":"https://openalex.org/W2613481459","doi":"https://doi.org/10.1515/cmam-2017-0054","mag":"2613481459"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2017-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0054","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0054/cmam-2017-0054.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0054/cmam-2017-0054.xml","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075602113","display_name":"J\u00e9r\u00f4me Droniou","orcid":"https://orcid.org/0000-0002-3339-3053"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"J\u00e9rome Droniou","raw_affiliation_strings":["School of Mathematical Sciences , Monash University , Clayton , Victoria 3800 , Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Monash University , Clayton , Victoria 3800 , Australia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019365126","display_name":"Neela Nataraj","orcid":"https://orcid.org/0000-0002-5180-459X"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Neela Nataraj","raw_affiliation_strings":["Department of Mathematics , Indian Institute of Technology Bombay , Powai , Mumbai 400076 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Indian Institute of Technology Bombay , Powai , Mumbai 400076 , India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018238948","display_name":"Devika Shylaja","orcid":"https://orcid.org/0000-0003-0919-9274"},"institutions":[{"id":"https://openalex.org/I2802772015","display_name":"IITB-Monash Research Academy","ror":"https://ror.org/02r3nf527","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531","https://openalex.org/I2802772015","https://openalex.org/I56590836"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Devika Shylaja","raw_affiliation_strings":["Department of Mathematics , IITB-Monash Research Academy , Powai , Mumbai 400076 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , IITB-Monash Research Academy , Powai , Mumbai 400076 , India","institution_ids":["https://openalex.org/I2802772015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019365126"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.2469,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52973235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"4","first_page":"609","last_page":"637"},"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":0.9994000196456909,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/discretization","display_name":"Discretization","score":0.7741597890853882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6680322885513306},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6523032784461975},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6346167325973511},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5648550391197205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5495855808258057},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5407102704048157},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.48379915952682495},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.47995948791503906},{"id":"https://openalex.org/keywords/von-neumann-stability-analysis","display_name":"Von Neumann stability analysis","score":0.4668933153152466},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.439129501581192},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4223829507827759},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4213234782218933},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41902607679367065},{"id":"https://openalex.org/keywords/control-variable","display_name":"Control variable","score":0.41449862718582153},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.3944234848022461},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37858426570892334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2741418182849884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25195440649986267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1822451949119568}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7741597890853882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6680322885513306},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6523032784461975},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6346167325973511},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5648550391197205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5495855808258057},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5407102704048157},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.48379915952682495},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.47995948791503906},{"id":"https://openalex.org/C71477052","wikidata":"https://www.wikidata.org/wiki/Q458556","display_name":"Von Neumann stability analysis","level":4,"score":0.4668933153152466},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.439129501581192},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4223829507827759},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4213234782218933},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41902607679367065},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.41449862718582153},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.3944234848022461},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37858426570892334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2741418182849884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25195440649986267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1822451949119568},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/cmam-2017-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0054","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0054/cmam-2017-0054.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1705.03256","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.03256","pdf_url":"https://arxiv.org/pdf/1705.03256","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:monash.edu:publications/4220180c-1f95-4839-ba42-95d6c787540f","is_oa":true,"landing_page_url":"https://research.monash.edu/en/publications/4220180c-1f95-4839-ba42-95d6c787540f","pdf_url":null,"source":{"id":"https://openalex.org/S4306402625","display_name":"Monash University Research Portal (Monash University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I56590836","host_organization_name":"Monash University","host_organization_lineage":["https://openalex.org/I56590836"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Droniou , J , Nataraj , N & Shylaja , D 2018 , ' Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method ' , Computational Methods in Applied Mathematics , vol. 18 , no. 4 , pp. 609-637 . https://doi.org/10.1515/cmam-2017-0054","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/cmam-2017-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0054","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0054/cmam-2017-0054.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"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/G645313901","display_name":null,"funder_award_id":"DP170100605","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W178921856","https://openalex.org/W1492746283","https://openalex.org/W1539280904","https://openalex.org/W1607053641","https://openalex.org/W1821352674","https://openalex.org/W1968754888","https://openalex.org/W1977135073","https://openalex.org/W1978282183","https://openalex.org/W1983938029","https://openalex.org/W2024466759","https://openalex.org/W2030948196","https://openalex.org/W2031821805","https://openalex.org/W2041304886","https://openalex.org/W2045526409","https://openalex.org/W2058059020","https://openalex.org/W2059162389","https://openalex.org/W2061861714","https://openalex.org/W2074783170","https://openalex.org/W2078576875","https://openalex.org/W2091525636","https://openalex.org/W2130763970","https://openalex.org/W2132729901","https://openalex.org/W2154745957","https://openalex.org/W2285931865","https://openalex.org/W2506719423","https://openalex.org/W2529476307","https://openalex.org/W2533536025","https://openalex.org/W2586787901","https://openalex.org/W2591235185","https://openalex.org/W2597248869","https://openalex.org/W2743553439","https://openalex.org/W3020991820","https://openalex.org/W3103539306","https://openalex.org/W4297968680","https://openalex.org/W4298157470","https://openalex.org/W4298228534","https://openalex.org/W6605495053"],"related_works":["https://openalex.org/W2169469906","https://openalex.org/W2134050719","https://openalex.org/W1996622347","https://openalex.org/W2330640442","https://openalex.org/W1990829983","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W3011379388","https://openalex.org/W2010592405","https://openalex.org/W1979699847"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"article":[2],"discusses":[3],"the":[4,24,84,88,92,120],"gradient":[5],"discretisation":[6],"method":[7],"(GDM)":[8],"for":[9,64,70,98,111],"distributed":[10],"optimal":[11,85],"control":[12,68,86],"problems":[13],"governed":[14],"by":[15],"diffusion":[16],"equation":[17],"with":[18],"pure":[19],"Neumann":[20],"boundary":[21],"condition.":[22],"Using":[23],"GDM":[25],"framework":[26],"enables":[27],"to":[28,35,48,52],"develop":[29],"an":[30],"analysis":[31],"that":[32],"directly":[33],"applies":[34],"a":[36,95,105],"wide":[37],"range":[38],"of":[39,94,123],"numerical":[40],"schemes,":[41],"from":[42],"conforming":[43],"and":[44,55,67,87,114],"non-conforming":[45,113],"finite":[46,50,53,57,116],"elements,":[47,51],"mixed":[49],"volumes":[54],"mimetic":[56,115],"differences":[58],"methods.":[59],"Optimal":[60],"order":[61],"error":[62],"estimates":[63],"state,":[65],"adjoint":[66,89],"variables":[69],"low-order":[71],"schemes":[72],"are":[73],"derived":[74],"under":[75],"standard":[76],"regularity":[77],"assumptions.":[78],"A":[79],"novel":[80],"projection":[81],"relation":[82],"between":[83],"variable":[90],"allows":[91],"proof":[93],"super-convergence":[96],"result":[97],"post-processed":[99],"control.":[100],"Numerical":[101],"experiments":[102],"performed":[103],"using":[104],"modified":[106],"active":[107],"set":[108],"strategy":[109],"algorithm":[110],"conforming,":[112],"difference":[117],"methods":[118],"confirm":[119],"theoretical":[121],"rates":[122],"convergence.":[124]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}