{"id":"https://openalex.org/W4390263052","doi":"https://doi.org/10.1007/s00211-023-01382-8","title":"Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates","display_name":"Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates","publication_year":2023,"publication_date":"2023-12-27","ids":{"openalex":"https://openalex.org/W4390263052","doi":"https://doi.org/10.1007/s00211-023-01382-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01382-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01382-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01382-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01382-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":["Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012391306","display_name":"Sophie Puttkammer","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sophie Puttkammer","raw_affiliation_strings":["Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.9422,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84994879,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"156","issue":"1","first_page":"1","last_page":"38"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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/algorithm","display_name":"Algorithm","score":0.7194762229919434},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5050812363624573},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42537909746170044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4211367964744568},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35708945989608765}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7194762229919434},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5050812363624573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42537909746170044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4211367964744568},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35708945989608765},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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":1,"locations":[{"id":"doi:10.1007/s00211-023-01382-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01382-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01382-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01382-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01382-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01382-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5285342013","display_name":null,"funder_award_id":"151/22","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5448639614","display_name":null,"funder_award_id":"CA 151/22-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8928656450","display_name":null,"funder_award_id":"Projekt DEAL","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323700","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390263052.pdf"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W253824085","https://openalex.org/W1585767079","https://openalex.org/W1968656190","https://openalex.org/W1970446082","https://openalex.org/W1970753375","https://openalex.org/W2012900529","https://openalex.org/W2019685695","https://openalex.org/W2025603126","https://openalex.org/W2029129352","https://openalex.org/W2033698269","https://openalex.org/W2039924562","https://openalex.org/W2042615888","https://openalex.org/W2044959876","https://openalex.org/W2056470693","https://openalex.org/W2058363312","https://openalex.org/W2059586807","https://openalex.org/W2062819342","https://openalex.org/W2063581353","https://openalex.org/W2072811159","https://openalex.org/W2074282379","https://openalex.org/W2082866666","https://openalex.org/W2084743165","https://openalex.org/W2092037996","https://openalex.org/W2096388839","https://openalex.org/W2107813568","https://openalex.org/W2110176271","https://openalex.org/W2122461891","https://openalex.org/W2137365186","https://openalex.org/W2157129549","https://openalex.org/W2172266329","https://openalex.org/W2293855717","https://openalex.org/W2321310861","https://openalex.org/W2527718086","https://openalex.org/W2592623476","https://openalex.org/W2765080741","https://openalex.org/W2802064869","https://openalex.org/W2962711883","https://openalex.org/W2963027749","https://openalex.org/W2963817075","https://openalex.org/W2964056873","https://openalex.org/W3000529065","https://openalex.org/W3004866040","https://openalex.org/W3034194306","https://openalex.org/W3143782910","https://openalex.org/W3158632992","https://openalex.org/W4211134967","https://openalex.org/W4250220742"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Abstract":[0],"Guaranteed":[1],"lower":[2],"Dirichlet":[3],"eigenvalue":[4],"bounds":[5],"(GLB)":[6],"can":[7],"be":[8],"computed":[9],"for":[10,53,114,133],"the":[11,54,62,76,95,100,115],"m":[12],"-th":[13],"Laplace":[14],"operator":[15],"with":[16,68],"a":[17,57,69,79,102,106,158],"recently":[18],"introduced":[19],"extra-stabilized":[20],"nonconforming":[21],"Crouzeix\u2013Raviart":[22],"(":[23,36],"$$m=1$$":[24],"<mml:math":[25,38,124],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[26,39,125],"<mml:mrow>":[27,40],"<mml:mi>m</mml:mi>":[28,41],"<mml:mo>=</mml:mo>":[29,42],"<mml:mn>1</mml:mn>":[30],"</mml:mrow>":[31,44],"</mml:math>":[32,45,130],")":[33,46],"or":[34],"Morley":[35],"$$m=2$$":[37],"<mml:mn>2</mml:mn>":[43,128],"finite":[47],"element":[48],"eigensolver.":[49],"Striking":[50],"numerical":[51],"evidence":[52],"superiority":[55],"of":[56,71,75,97,117,138,143,147,161],"new":[58,159],"adaptive":[59,149],"eigensolver":[60],"motivates":[61],"convergence":[63,73,104,145],"analysis":[64,108,142],"in":[65,111,154],"this":[66,112],"paper":[67,113],"proof":[70,83,116],"optimal":[72,144],"rates":[74,146],"GLB":[77],"towards":[78],"simple":[80],"eigenvalue.":[81],"The":[82,141],"is":[84,109,152],"based":[85],"on":[86],"(a":[87],"generalization":[88],"of)":[89],"known":[90,101],"abstract":[91],"arguments":[92],"entitled":[93],"as":[94],"axioms":[96],"adaptivity.":[98],"Beyond":[99],"priori":[103],"rates,":[105],"medius":[107],"enfolded":[110],"best-approximation":[118],"results.":[119],"This":[120],"and":[121,156],"subordinated":[122],"$$L^2$$":[123],"<mml:msup>":[126],"<mml:mi>L</mml:mi>":[127],"</mml:msup>":[129],"error":[131],"estimates":[132],"locally":[134],"refined":[135],"triangulations":[136],"appear":[137],"independent":[139],"interest.":[140],"an":[148],"mesh-refining":[150],"algorithm":[151],"performed":[153],"3D":[155],"highlights":[157],"version":[160],"discrete":[162],"reliability.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}