{"id":"https://openalex.org/W2952125423","doi":"https://doi.org/10.1137/140958554","title":"A Study on Anisotropic Mesh Adaptation for Finite Element Approximation of Eigenvalue Problems with Anisotropic Diffusion Operators","display_name":"A Study on Anisotropic Mesh Adaptation for Finite Element Approximation of Eigenvalue Problems with Anisotropic Diffusion Operators","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2952125423","doi":"https://doi.org/10.1137/140958554","mag":"2952125423"},"language":"en","primary_location":{"id":"doi:10.1137/140958554","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958554","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1402.6001","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101692077","display_name":"Jingyue Wang","orcid":"https://orcid.org/0000-0002-3896-5137"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jingyue Wang","raw_affiliation_strings":["Department of Mathematics, the University of Kansas, Lawrence, KS 66045, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, the University of Kansas, Lawrence, KS 66045, U.S.A","institution_ids":["https://openalex.org/I146416000"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041682967","display_name":"Weizhang Huang","orcid":"https://orcid.org/0000-0002-7510-8230"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weizhang Huang","raw_affiliation_strings":["Department of Mathematics, the University of Kansas, Lawrence, KS 66045, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, the University of Kansas, Lawrence, KS 66045, U.S.A","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I146416000"],"apc_list":null,"apc_paid":null,"fwci":0.2886,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64070163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"37","issue":"6","first_page":"A2924","last_page":"A2946"},"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":0.9973999857902527,"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":0.9958999752998352,"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/mathematics","display_name":"Mathematics","score":0.7017048597335815},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6365980505943298},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.587658166885376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5683755874633789},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.48543959856033325},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.472817063331604},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45007258653640747},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4194904863834381},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3670925796031952},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12376219034194946}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7017048597335815},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6365980505943298},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.587658166885376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5683755874633789},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48543959856033325},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.472817063331604},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45007258653640747},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4194904863834381},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3670925796031952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12376219034194946},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140958554","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958554","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.6001","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1402.6001","pdf_url":"https://arxiv.org/pdf/1402.6001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1402.6001","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1402.6001","pdf_url":"https://arxiv.org/pdf/1402.6001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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/G2925039622","display_name":"Topics in anisotropic mesh adaptation and application to anisotropic diffusion problems","funder_award_id":"1115118","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/W2952125423.pdf","grobid_xml":"https://content.openalex.org/works/W2952125423.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W53208737","https://openalex.org/W104028471","https://openalex.org/W118271839","https://openalex.org/W278206857","https://openalex.org/W597568752","https://openalex.org/W1480546554","https://openalex.org/W1573835018","https://openalex.org/W1648384598","https://openalex.org/W1757993260","https://openalex.org/W1963839729","https://openalex.org/W1963872100","https://openalex.org/W1977602497","https://openalex.org/W1979518155","https://openalex.org/W1979821272","https://openalex.org/W1979972914","https://openalex.org/W1981792545","https://openalex.org/W1987022010","https://openalex.org/W1992459887","https://openalex.org/W1996440217","https://openalex.org/W2000082576","https://openalex.org/W2007738137","https://openalex.org/W2009941208","https://openalex.org/W2022088322","https://openalex.org/W2023729193","https://openalex.org/W2026313996","https://openalex.org/W2026620757","https://openalex.org/W2041568728","https://openalex.org/W2043570590","https://openalex.org/W2056604279","https://openalex.org/W2062599983","https://openalex.org/W2068079525","https://openalex.org/W2069426867","https://openalex.org/W2069640730","https://openalex.org/W2071415238","https://openalex.org/W2071582219","https://openalex.org/W2085045785","https://openalex.org/W2089181715","https://openalex.org/W2095636304","https://openalex.org/W2103975664","https://openalex.org/W2114253824","https://openalex.org/W2115218270","https://openalex.org/W2119066628","https://openalex.org/W2120398992","https://openalex.org/W2143496291","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2150242204","https://openalex.org/W2151128814","https://openalex.org/W2153407748","https://openalex.org/W2157129549","https://openalex.org/W2157670588","https://openalex.org/W2230101480","https://openalex.org/W2325448729","https://openalex.org/W2615932191","https://openalex.org/W2962831842","https://openalex.org/W3011612142","https://openalex.org/W3103648785","https://openalex.org/W4231910423","https://openalex.org/W4242353639"],"related_works":["https://openalex.org/W2794789911","https://openalex.org/W4298134547","https://openalex.org/W2122976425","https://openalex.org/W2088773039","https://openalex.org/W4382753160","https://openalex.org/W2284229495","https://openalex.org/W2921748058","https://openalex.org/W4380570985","https://openalex.org/W2133690079","https://openalex.org/W2111215486"],"abstract_inverted_index":{"Anisotropic":[0],"mesh":[1,20,28,141,197],"adaptation":[2],"is":[3,22,29,110,129,136,178,212],"studied":[4,131],"for":[5,54,200],"the":[6,37,46,49,61,102,107,113,124,139,145,148,160,166,169,172,179,182,185,195,207,216],"linear":[7],"finite":[8,173],"element":[9,174],"solution":[10],"of":[11,106,118,120,126,147,162,168,171,181,209,221],"eigenvalue":[12,127,210],"problems":[13,70,128,211],"with":[14,24],"anisotropic":[15,83],"diffusion":[16,69],"operators.":[17],"The":[18,116],"$\\mathbb{M}$-uniform":[19],"approach":[21],"employed":[23],"which":[25],"any":[26],"nonuniform":[27],"characterized":[30],"mathematically":[31],"as":[32],"a":[33,41],"uniform":[34,94],"one":[35],"in":[36,48,71,132,184,194],"metric":[38,42],"specified":[39],"by":[40,112],"tensor.":[43],"Bounds":[44],"on":[45,64,123],"error":[47,108,170],"computed":[50,91],"eigenvalues":[51,92],"are":[52,77,198],"established":[53],"quasi-$\\mathbb{M}$-uniform":[55],"meshes.":[56,98],"Numerical":[57,79],"examples":[58],"arising":[59],"from":[60],"Laplace--Beltrami":[62],"operator":[63],"parameterized":[65],"surfaces":[66],"and":[67,74],"nonlinear":[68],"image":[72],"processing":[73],"radiation":[75],"hydrodynamics":[76],"presented.":[78],"results":[80],"show":[81],"that":[82,109,138,206,220],"adaptive":[84,97,187],"meshes":[85],"can":[86],"lead":[87],"to":[88,143,158,215],"more":[89,213],"accurate":[90],"than":[93,219],"or":[95],"isotropic":[96],"They":[99],"also":[100,130],"confirm":[101],"second":[103],"order":[104],"convergence":[105],"predicted":[111],"theoretical":[114],"analysis.":[115],"effects":[117,161],"approximation":[119,164,218],"curved":[121],"boundaries":[122],"computation":[125,208],"two":[133],"dimensions.":[134],"It":[135],"shown":[137],"initial":[140,196],"used":[142],"define":[144],"geometry":[146],"physical":[149],"domain":[150],"should":[151],"contain":[152],"at":[153,165],"least":[154],"$\\sqrt{N}$":[155],"boundary":[156,163,192,201,217,222],"points":[157,193],"keep":[159],"level":[167],"approximation,":[175],"where":[176],"$N$":[177],"number":[180],"elements":[183],"final":[186],"mesh.":[188],"Only":[189],"about":[190],"$\\sqrt[3]{N}$":[191],"needed":[199],"value":[202,223],"problems.":[203,224],"This":[204],"implies":[205],"sensitive":[214]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}