{"id":"https://openalex.org/W2192442929","doi":"https://doi.org/10.1137/15m1036877","title":"Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters","display_name":"Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2192442929","doi":"https://doi.org/10.1137/15m1036877","mag":"2192442929"},"language":"en","primary_location":{"id":"doi:10.1137/15m1036877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1036877","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1508.06265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057355391","display_name":"Andrea Bonito","orcid":"https://orcid.org/0000-0002-0236-6909"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrea Bonito","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070767719","display_name":"Alan Demlow","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan Demlow","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057355391"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00241887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"4","first_page":"2379","last_page":"2388"},"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":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.7781460881233215},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7579914331436157},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.66510409116745},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6430907249450684},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.641983687877655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5891555547714233},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5868281126022339},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5025112628936768},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4695131480693817},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3579065203666687},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.2922460436820984},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.13879898190498352},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08632016181945801}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7781460881233215},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7579914331436157},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.66510409116745},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6430907249450684},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.641983687877655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5891555547714233},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5868281126022339},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5025112628936768},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4695131480693817},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3579065203666687},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2922460436820984},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.13879898190498352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08632016181945801},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1036877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1036877","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"},{"id":"pmh:oai:arXiv.org:1508.06265","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.06265","pdf_url":"https://arxiv.org/pdf/1508.06265","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":"mag:2192442929","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1508.06265.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/180685","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/180685","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.1508.06265","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.06265","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1508.06265","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.06265","pdf_url":"https://arxiv.org/pdf/1508.06265","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1373826664","display_name":null,"funder_award_id":"DMS-1518925","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4494125632","display_name":null,"funder_award_id":"DMS-1254618","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2192442929.pdf","grobid_xml":"https://content.openalex.org/works/W2192442929.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1981792545","https://openalex.org/W2009941208","https://openalex.org/W2025603126","https://openalex.org/W2029129352","https://openalex.org/W2039924562","https://openalex.org/W2042615888","https://openalex.org/W2044959876","https://openalex.org/W2056470693","https://openalex.org/W2068079525","https://openalex.org/W2072811159","https://openalex.org/W2084743165","https://openalex.org/W2094648722","https://openalex.org/W2100950337","https://openalex.org/W2102295719","https://openalex.org/W2107813568","https://openalex.org/W2130724727","https://openalex.org/W2527718086","https://openalex.org/W2964192538"],"related_works":["https://openalex.org/W2964114492","https://openalex.org/W30647803","https://openalex.org/W2084780726","https://openalex.org/W2089768471","https://openalex.org/W2949622080","https://openalex.org/W764222646","https://openalex.org/W2611078623","https://openalex.org/W2502050875","https://openalex.org/W2953290261","https://openalex.org/W2594541596","https://openalex.org/W2617106772","https://openalex.org/W2884228451","https://openalex.org/W2311203337","https://openalex.org/W2227962568","https://openalex.org/W2790726926","https://openalex.org/W2550234095","https://openalex.org/W2790683262","https://openalex.org/W3003890753","https://openalex.org/W2962381865","https://openalex.org/W3113292938"],"abstract_inverted_index":{"Proofs":[0],"of":[1,3,14,58,62,144,155,184,213,216,222],"convergence":[2,55,80],"adaptive":[4,177],"finite":[5,123,134],"element":[6,124,135],"methods":[7],"(AFEMs)":[8],"for":[9,32,60,77,112,116,161,179],"approximating":[10],"eigenvalues":[11,36,61,181],"and":[12,34,42,56,147,149,158],"eigenfunctions":[13],"linear":[15,122],"elliptic":[16],"problems":[17],"have":[18],"been":[19],"given":[20],"in":[21,28,44,201,233],"several":[22],"recent":[23],"papers.":[24],"A":[25],"key":[26,171,197],"step":[27],"establishing":[29],"such":[30],"results":[31,224],"multiple":[33],"clustered":[35,162,180],"was":[37,69],"provided":[38],"by":[39],"Dai,":[40,145],"He,":[41,146],"Zhou":[43,148],"[IMA":[45],"J.":[46],"Numer.":[47],"Anal.,":[48],"35":[49],"(2015),":[50,98],"pp.":[51,99],"1934--1977],":[52],"who":[53],"proved":[54],"optimality":[57],"AFEMs":[59],"multiplicity":[63],"greater":[64],"than":[65],"one.":[66],"There":[67],"it":[68],"shown":[70],"that":[71,108,175,195,237],"a":[72,86,103,109,196,226],"theoretical":[73,159],"(noncomputable)":[74],"error":[75],"estimator":[76,89],"which":[78],"standard":[79,87,110,176],"proofs":[81],"apply":[82],"is":[83,240],"equivalent":[84],"to":[85,106,235],"computable":[88],"on":[90,229],"sufficiently":[91,241],"fine":[92],"grids.":[93],"In":[94,164],"[Numer.":[95],"Math.,":[96],"130":[97],"467--496],":[100],"Gallistl":[101,150],"used":[102],"similar":[104],"tool":[105],"prove":[107],"AFEM":[111],"controlling":[113],"eigenvalue":[114,219],"clusters":[115],"the":[117,142,156,202,204,214,217,230,238],"Laplacian":[118],"using":[119],"continuous":[120],"piecewise":[121],"spaces":[125,136],"converges":[126],"with":[127,189],"optimal":[128,190],"rate.":[129,191],"When":[130],"considering":[131],"either":[132],"higher-order":[133],"or":[137],"nonconstant":[138],"diffusion":[139],"coefficients,":[140],"however,":[141],"arguments":[143],"do":[151],"not":[152],"yield":[153],"equivalence":[154],"practical":[157],"estimators":[160],"eigenvalues.":[163],"this":[165,169],"article":[166],"we":[167],"provide":[168],"missing":[170],"step,":[172],"thus":[173],"showing":[174],"FEMs":[178],"employing":[182],"elements":[183],"arbitrary":[185],"polynomial":[186],"degree":[187],"converge":[188],"We":[192],"additionally":[193],"establish":[194],"user-defined":[198],"input":[199],"parameter":[200],"AFEM,":[203],"bulk":[205],"marking":[206],"parameter,":[207],"may":[208],"be":[209],"chosen":[210],"entirely":[211],"independently":[212],"properties":[215],"target":[218],"cluster.":[220],"All":[221],"these":[223],"assume":[225],"fineness":[227],"condition":[228],"initial":[231],"mesh":[232],"order":[234],"ensure":[236],"nonlinearity":[239],"resolved.":[242]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}