{"id":"https://openalex.org/W1974791647","doi":"https://doi.org/10.1137/120880884","title":"Convergence Analysis of All-at-Once Multigrid Methods for Elliptic Control Problems under Partial Elliptic Regularity","display_name":"Convergence Analysis of All-at-Once Multigrid Methods for Elliptic Control Problems under Partial Elliptic Regularity","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1974791647","doi":"https://doi.org/10.1137/120880884","mag":"1974791647"},"language":"en","primary_location":{"id":"doi:10.1137/120880884","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120880884","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5047452055","display_name":"Stefan Takacs","orcid":"https://orcid.org/0000-0003-3496-7650"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Takacs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029325851","display_name":"Walter Zulehner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walter Zulehner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5273,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.91762659,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"3","first_page":"1853","last_page":"1874"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9948999881744385,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8242242336273193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8038601875305176},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6413208246231079},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6005436778068542},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5351769328117371},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5149381756782532},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.49277809262275696},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.47863641381263733},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.42226406931877136},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.41819262504577637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.332920104265213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32007139921188354}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8242242336273193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8038601875305176},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6413208246231079},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6005436778068542},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5351769328117371},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5149381756782532},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.49277809262275696},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47863641381263733},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.42226406931877136},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.41819262504577637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.332920104265213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32007139921188354},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120880884","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120880884","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W203115219","https://openalex.org/W591292934","https://openalex.org/W1502992081","https://openalex.org/W1509550030","https://openalex.org/W1597209545","https://openalex.org/W1604809219","https://openalex.org/W1978837662","https://openalex.org/W1989116194","https://openalex.org/W2011913964","https://openalex.org/W2059880466","https://openalex.org/W2062226392","https://openalex.org/W2127981460"],"related_works":["https://openalex.org/W2356816331","https://openalex.org/W2307054062","https://openalex.org/W322277319","https://openalex.org/W2344267562","https://openalex.org/W1984227015","https://openalex.org/W2042128780","https://openalex.org/W1632720046","https://openalex.org/W1566351512","https://openalex.org/W364294403","https://openalex.org/W2054004413"],"abstract_inverted_index":{"In":[0],"this":[1,59],"paper":[2],"we":[3,42],"consider":[4],"the":[5,63,67,78],"convergence":[6],"theory":[7],"for":[8,13,77],"an":[9,20],"all-at-once":[10],"multigrid":[11],"method":[12],"a":[14,44,51],"distributed":[15],"optimal":[16],"control":[17],"problem.":[18],"Such":[19],"analysis":[21,68],"has":[22],"been":[23],"recently":[24],"done":[25],"[J.":[26],"Sch\u00f6berl,":[27],"R.":[28],"Simon,":[29],"and":[30],"W.":[31],"Zulehner,":[32],"SIAM":[33],"J.":[34],"Numer.":[35],"Anal.,":[36],"49":[37],"(2011),":[38],"pp.":[39],"1482--1503].":[40],"Here,":[41],"give":[43],"new":[45,60],"proof":[46],"which":[47],"is":[48,62],"based":[49],"on":[50],"more":[52],"straightforward":[53],"approach.":[54],"The":[55],"main":[56],"benefit":[57],"of":[58],"approach":[61],"possibility":[64],"to":[65,69],"extend":[66],"domains":[70],"where":[71],"full":[72],"elliptic":[73],"regularity,":[74],"i.e.,":[75],"$H^2$-regularity":[76],"Poisson":[79],"problem,":[80],"cannot":[81],"be":[82],"guaranteed.":[83]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
