{"id":"https://openalex.org/W2026313996","doi":"https://doi.org/10.1137/s0036142997320164","title":"A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems","display_name":"A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2026313996","doi":"https://doi.org/10.1137/s0036142997320164","mag":"2026313996"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142997320164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997320164","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/A5077614976","display_name":"Mats G. Larson","orcid":"https://orcid.org/0000-0001-5589-4521"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mats G. Larson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077614976"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7691,"has_fulltext":false,"cited_by_count":133,"citation_normalized_percentile":{"value":0.88980994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"38","issue":"2","first_page":"608","last_page":"625"},"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":0.9983000159263611,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.8673022985458374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8062236309051514},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7497501969337463},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.672594428062439},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6299526691436768},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5699589848518372},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.540759265422821},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5052323937416077},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4545899033546448},{"id":"https://openalex.org/keywords/a-priori-estimate","display_name":"A priori estimate","score":0.4394703507423401},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3299809992313385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20157137513160706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09512108564376831}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.8673022985458374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8062236309051514},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7497501969337463},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.672594428062439},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6299526691436768},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5699589848518372},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.540759265422821},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5052323937416077},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4545899033546448},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.4394703507423401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3299809992313385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20157137513160706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09512108564376831},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142997320164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997320164","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:bibcyt.ucla.edu.ve:T070300010721/13","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010721/13&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.5400000214576721,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1593553932","https://openalex.org/W1866311589","https://openalex.org/W1964725324","https://openalex.org/W1972593045","https://openalex.org/W1979254596","https://openalex.org/W1988552931","https://openalex.org/W1990669907","https://openalex.org/W2009985306","https://openalex.org/W2013737143","https://openalex.org/W2044355921","https://openalex.org/W2071036364","https://openalex.org/W2076458295","https://openalex.org/W2082621526","https://openalex.org/W2092910485","https://openalex.org/W2122602456","https://openalex.org/W2148639620","https://openalex.org/W2150175359","https://openalex.org/W3022136271","https://openalex.org/W4242273588","https://openalex.org/W4247003349","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2155768045","https://openalex.org/W2388419667","https://openalex.org/W1997485274","https://openalex.org/W1950058236","https://openalex.org/W2413880911","https://openalex.org/W2362625355","https://openalex.org/W4292720219","https://openalex.org/W2286756406","https://openalex.org/W2963076594","https://openalex.org/W4300056801"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,24,63,93,120,142,150,156,165],"new":[3],"error":[4,29,37,54,144,152,176],"analysis":[5,16,161],"for":[6,27,174],"finite":[7],"element":[8],"approximations":[9],"of":[10,18,59,86,96,101,104,114,123,128,130,148,180],"self-adjoint":[11],"elliptic":[12],"eigenvalue":[13],"problems.":[14],"The":[15,36,79,160],"consists":[17],"three":[19],"steps.":[20],"First":[21],"we":[22,91,117,139],"prove":[23,118],"posteriori":[25,151,166],"estimates":[26,52,145,153,167],"the":[28,31,39,45,53,60,67,72,76,87,102,105,108,112,124,131,135,149,155,164],"in":[30,38,44,57,99,126],"approximate":[32,73],"eigenvectors":[33,40,133],"and":[34,47,66,90,111,134,170,178],"eigenvalues.":[35],"is":[41,55],"measured":[42],"both":[43],"L2":[46],"energy":[48],"norms.":[49],"In":[50],"these":[51],"bounded":[56],"terms":[58,100,127],"mesh":[61,109,136],"size,":[62,110],"stability":[64,80,84],"factor,":[65],"residual,":[68],"obtained":[69],"by":[70,146],"inserting":[71],"eigenpair":[74],"into":[75],"differential":[77],"equation.":[78],"factor":[81],"describes":[82],"relevant":[83],"properties":[85],"continuous":[88,106],"problem":[89],"give":[92],"precise":[94,141],"estimate":[95,122],"its":[97],"size":[98],"spectrum":[103],"problem,":[107],"choice":[113],"norm.":[115],"Next":[116],"an":[119],"priori":[121,143,157],"residual":[125,158],"derivatives":[129],"exact":[132],"size.":[137],"Finally":[138],"obtain":[140],"combination":[147],"with":[154],"estimate.":[159],"shows":[162],"that":[163],"are":[168],"optimal":[169],"may":[171],"be":[172],"used":[173],"quantitative":[175],"estimation":[177],"design":[179],"adaptive":[181],"algorithms.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
