{"id":"https://openalex.org/W2011637759","doi":"https://doi.org/10.1137/080742737","title":"Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in $R^N$, $N\\geq2$. I: Local Interior Expansions","display_name":"Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in $R^N$, $N\\geq2$. I: Local Interior Expansions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2011637759","doi":"https://doi.org/10.1137/080742737","mag":"2011637759"},"language":"en","primary_location":{"id":"doi:10.1137/080742737","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742737","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":true,"oa_status":"green","oa_url":"http://publications.lib.chalmers.se/records/fulltext/103183/local_103183.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040028686","display_name":"Mohammad Asadzadeh","orcid":"https://orcid.org/0000-0002-9151-1505"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. Asadzadeh","raw_affiliation_strings":["mohammad@chalmers.se#TAB#"],"affiliations":[{"raw_affiliation_string":"mohammad@chalmers.se#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052440884","display_name":"A. H. Schatz","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. H. Schatz","raw_affiliation_strings":["schatz@math.cornell.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"schatz@math.cornell.edu#TAB#","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046208678","display_name":"Wolfgang L. Wendland","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. Wendland","raw_affiliation_strings":["wendland@mathematik.uni-stuttgart.de#TAB#"],"affiliations":[{"raw_affiliation_string":"wendland@mathematik.uni-stuttgart.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040028686"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6864,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.71753759,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"5","first_page":"2000","last_page":"2017"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9961000084877014,"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":0.9939000010490417,"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":0.8195250630378723},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6279608011245728},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.615468442440033},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.602699339389801},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4875792860984802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4849834442138672},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.46863484382629395},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.41719263792037964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40238136053085327},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1720627248287201},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07482397556304932}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8195250630378723},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6279608011245728},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.615468442440033},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.602699339389801},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4875792860984802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4849834442138672},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.46863484382629395},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41719263792037964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40238136053085327},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1720627248287201},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07482397556304932},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080742737","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742737","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:research.chalmers.se:103183","is_oa":true,"landing_page_url":"https://research.chalmers.se/en/publication/103183","pdf_url":"http://publications.lib.chalmers.se/records/fulltext/103183/local_103183.pdf","source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:research.chalmers.se:103183","is_oa":true,"landing_page_url":"https://research.chalmers.se/en/publication/103183","pdf_url":"http://publications.lib.chalmers.se/records/fulltext/103183/local_103183.pdf","source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320940","display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning","ror":"https://ror.org/044wr7g58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2011637759.pdf","grobid_xml":"https://content.openalex.org/works/W2011637759.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W73179330","https://openalex.org/W168254716","https://openalex.org/W919962423","https://openalex.org/W1589236075","https://openalex.org/W1967959056","https://openalex.org/W1982511487","https://openalex.org/W1992125889","https://openalex.org/W2006453627","https://openalex.org/W2007751122","https://openalex.org/W2010332082","https://openalex.org/W2014866425","https://openalex.org/W2036333759","https://openalex.org/W2054558075","https://openalex.org/W2057987812","https://openalex.org/W2061937382","https://openalex.org/W2062383984","https://openalex.org/W2065279412","https://openalex.org/W2065479689","https://openalex.org/W2070008014","https://openalex.org/W2074500917","https://openalex.org/W2075085615","https://openalex.org/W2086538707","https://openalex.org/W2087750281","https://openalex.org/W2161591838","https://openalex.org/W3002375416"],"related_works":["https://openalex.org/W2055836843","https://openalex.org/W2380000090","https://openalex.org/W2755775996","https://openalex.org/W2374797863","https://openalex.org/W2773728674","https://openalex.org/W2349308527","https://openalex.org/W3131818128","https://openalex.org/W2069701013","https://openalex.org/W2366062865","https://openalex.org/W2502632608"],"abstract_inverted_index":{"Our":[0],"aim":[1],"here":[2],"is":[3],"to":[4],"give":[5],"sufficient":[6],"conditions":[7],"on":[8],"the":[9,18,21,26,32,41,55],"finite":[10,22],"element":[11,23],"spaces":[12],"near":[13],"a":[14],"point":[15,33],"so":[16],"that":[17],"error":[19],"in":[20,38,61,68],"method":[24],"for":[25,46,63],"function":[27],"and":[28,75],"its":[29],"derivatives":[30],"at":[31],"have":[34],"exact":[35],"asymptotic":[36,57],"expansions":[37,51],"terms":[39],"of":[40],"mesh":[42],"parameter":[43],"h,":[44],"valid":[45,60],"h":[47],"sufficiently":[48],"small.":[49],"Such":[50],"are":[52],"obtained":[53],"from":[54],"so-called":[56],"expansion":[58],"inequalities":[59],"$\\mathbf{R}^N$":[62],"$N\\geq2$,":[64],"studies":[65],"by":[66],"Schatz":[67],"[Math.":[69],"Comp.,":[70],"67":[71],"(1998),":[72],"pp.":[73,82],"877\u2013899]":[74],"[SIAM":[76],"J.":[77],"Numer.":[78],"Anal.,":[79],"38":[80],"(2000),":[81],"1269\u20131293].":[83]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}