{"id":"https://openalex.org/W2781931364","doi":"https://doi.org/10.1137/17m1163311","title":"A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace--Beltrami Operator","display_name":"A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace--Beltrami Operator","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2781931364","doi":"https://doi.org/10.1137/17m1163311","mag":"2781931364"},"language":"en","primary_location":{"id":"doi:10.1137/17m1163311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1163311","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/1801.00197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110288561","display_name":"Andrea Bonito","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrea Bonito","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","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":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063084470","display_name":"Justin Owen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Justin Owen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110288561"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00750454,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"56","issue":"5","first_page":"2963","last_page":"2988"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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":0.9991000294685364,"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/eigenfunction","display_name":"Eigenfunction","score":0.7401440739631653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7111293077468872},{"id":"https://openalex.org/keywords/laplace\u2013beltrami-operator","display_name":"Laplace\u2013Beltrami operator","score":0.6086987853050232},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6012051105499268},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5733875036239624},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5397160649299622},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5303968191146851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4395739436149597},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43906843662261963},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4352788031101227},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.25003767013549805},{"id":"https://openalex.org/keywords/p-laplacian","display_name":"p-Laplacian","score":0.13278642296791077},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.11683443188667297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10121616721153259},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0807417631149292}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7401440739631653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7111293077468872},{"id":"https://openalex.org/C49747540","wikidata":"https://www.wikidata.org/wiki/Q1071846","display_name":"Laplace\u2013Beltrami operator","level":4,"score":0.6086987853050232},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6012051105499268},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5733875036239624},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5397160649299622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5303968191146851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4395739436149597},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43906843662261963},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4352788031101227},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.25003767013549805},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.13278642296791077},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.11683443188667297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10121616721153259},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0807417631149292},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1163311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1163311","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:1801.00197","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.00197","pdf_url":"https://arxiv.org/pdf/1801.00197","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:2781931364","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1801.00197.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":"doi:10.48550/arxiv.1801.00197","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.00197","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:1801.00197","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.00197","pdf_url":"https://arxiv.org/pdf/1801.00197","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/G1715314055","display_name":null,"funder_award_id":"DMS-120369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2945280966","display_name":null,"funder_award_id":"1254618","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"},{"id":"https://openalex.org/G5692145523","display_name":"Topics in Mathematical Theory of Adaptive Finite Element Methods","funder_award_id":"1720369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5967800407","display_name":"Problems in mathematical foundations of adaptive finite element methods","funder_award_id":"1518925","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6594959862","display_name":null,"funder_award_id":"DMS-1720369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7088784768","display_name":null,"funder_award_id":"DMS-154618","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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/W2781931364.pdf","grobid_xml":"https://content.openalex.org/works/W2781931364.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W591292934","https://openalex.org/W1498345005","https://openalex.org/W1550152218","https://openalex.org/W1981792545","https://openalex.org/W1982274529","https://openalex.org/W2005005412","https://openalex.org/W2009941208","https://openalex.org/W2023576489","https://openalex.org/W2025603126","https://openalex.org/W2030797443","https://openalex.org/W2034024171","https://openalex.org/W2042615888","https://openalex.org/W2043377185","https://openalex.org/W2043942062","https://openalex.org/W2044355921","https://openalex.org/W2046573877","https://openalex.org/W2053893280","https://openalex.org/W2057292049","https://openalex.org/W2063970390","https://openalex.org/W2063974361","https://openalex.org/W2065479689","https://openalex.org/W2068079525","https://openalex.org/W2077485422","https://openalex.org/W2102295719","https://openalex.org/W2103975664","https://openalex.org/W2106917647","https://openalex.org/W2113048348","https://openalex.org/W2120398992","https://openalex.org/W2170429437","https://openalex.org/W2330663406","https://openalex.org/W2527718086","https://openalex.org/W2964114492","https://openalex.org/W2964290469"],"related_works":["https://openalex.org/W3004789150","https://openalex.org/W1967420868","https://openalex.org/W2552336182","https://openalex.org/W2058338453","https://openalex.org/W3084942782","https://openalex.org/W2012970755","https://openalex.org/W2413969096","https://openalex.org/W134272123","https://openalex.org/W12316911","https://openalex.org/W3042764647","https://openalex.org/W1982389294","https://openalex.org/W2119640668","https://openalex.org/W624920875","https://openalex.org/W3176358960","https://openalex.org/W2124841882","https://openalex.org/W2084992488","https://openalex.org/W2993429205","https://openalex.org/W2065369632","https://openalex.org/W3100056802","https://openalex.org/W2633985543"],"abstract_inverted_index":{"Elliptic":[0],"partial":[1],"differential":[2],"equations":[3],"on":[4,123],"surfaces":[5],"play":[6],"an":[7],"essential":[8],"role":[9],"in":[10,148],"geometry,":[11],"relativity":[12],"theory,":[13],"phase":[14],"transitions,":[15],"materials":[16],"science,":[17],"image":[18],"processing,":[19],"and":[20,33,73],"other":[21],"applications.":[22],"They":[23],"are":[24],"typically":[25],"governed":[26],"by":[27,36,57],"the":[28,43,62,68,71,74,97,112,119,124,132,136,149],"Laplace--Beltrami":[29,44],"operator.":[30],"We":[31,84],"present":[32],"analyze":[34],"approximations":[35,94],"surface":[37,72],"finite":[38,79],"element":[39,80],"methods":[40],"(SFEM)":[41],"of":[42,60,70,82,118,126,156],"eigenvalue":[45],"problem.":[46,99],"As":[47],"for":[48,50,92,96,104,111],"SFEM":[49],"source":[51,98],"problems,":[52],"spectral":[53],"approximation":[54,69],"is":[55,102],"challenged":[56],"two":[58,88],"sources":[59,90],"errors:":[61],"geometric":[63,113,120,137],"consistency":[64,114,138],"error":[65,76,89,121],"due":[66],"to":[67,78,130,144],"Galerkin":[75],"corresponding":[77],"resolution":[81],"eigenfunctions.":[83],"show":[85],"that":[86],"these":[87],"interact":[91],"eigenfunction":[93,150],"as":[95],"The":[100,116],"situation":[101,109],"different":[103],"eigenvalues,":[105],"where":[106],"a":[107,153],"novel":[108],"occurs":[110],"error:":[115],"degree":[117],"depends":[122],"choice":[125,155],"interpolation":[127,157],"points":[128],"used":[129],"construct":[131],"approximate":[133],"surface.":[134],"Thus":[135],"term":[139],"can":[140],"sometimes":[141],"be":[142],"made":[143],"converge":[145],"faster":[146],"than":[147],"case":[151],"through":[152],"judicious":[154],"points.":[158]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}