{"id":"https://openalex.org/W2121031654","doi":"https://doi.org/10.1090/s0025-5718-2011-02546-9","title":"Best approximation property in the \ud835\udc4a\u00b9_{\u221e} norm for finite element methods on graded meshes","display_name":"Best approximation property in the \ud835\udc4a\u00b9_{\u221e} norm for finite element methods on graded meshes","publication_year":2011,"publication_date":"2011-09-29","ids":{"openalex":"https://openalex.org/W2121031654","doi":"https://doi.org/10.1090/s0025-5718-2011-02546-9","mag":"2121031654"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02546-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02546-9","pdf_url":"https://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02546-9/S0025-5718-2011-02546-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02546-9/S0025-5718-2011-02546-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070767719","display_name":"Alan Demlow","orcid":null},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Demlow","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016780750","display_name":"Dmitriy Leykekhman","orcid":"https://orcid.org/0000-0001-9643-5540"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Leykekhman","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269","Department of Mathematics , University of Connecticut Storrs , Connecticut, 06269"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of Mathematics , University of Connecticut Storrs , Connecticut, 06269","institution_ids":["https://openalex.org/I140172145"]}]},{"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. Schatz","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, New York 14853","\u00a7Department of Mathematics, Cornell University, Ithaca, New York 14853"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"\u00a7Department of Mathematics, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108406032","display_name":"Lars B. Wahlbin","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":"L. Wahlbin","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, New York 14853","\u00a7Department of Mathematics, Cornell University, Ithaca, New York 14853"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"\u00a7Department of Mathematics, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4663,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.88898761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"81","issue":"278","first_page":"743","last_page":"764"},"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":0.9958999752998352,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9955000281333923,"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/polygon-mesh","display_name":"Polygon mesh","score":0.8784219622612},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8468862771987915},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.715899646282196},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6990560293197632},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6768049597740173},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6132082939147949},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5240235924720764},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43472376465797424},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4032078981399536},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3222442865371704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3168810307979584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17725273966789246}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8784219622612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468862771987915},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.715899646282196},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6990560293197632},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6768049597740173},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6132082939147949},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5240235924720764},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43472376465797424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4032078981399536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3222442865371704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3168810307979584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17725273966789246},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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":1,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02546-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02546-9","pdf_url":"https://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02546-9/S0025-5718-2011-02546-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02546-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02546-9","pdf_url":"https://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02546-9/S0025-5718-2011-02546-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G5914972424","display_name":"Algorithms and Numerical Analysis for Partial Differential Equations","funder_award_id":"0612599","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7548561726","display_name":"Discontinuous Galerkin Methods for Optimal Control Problems Governed by Advection-Diffusion Equations","funder_award_id":"0811167","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/W2121031654.pdf","grobid_xml":"https://content.openalex.org/works/W2121031654.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W94976795","https://openalex.org/W431928912","https://openalex.org/W1565460255","https://openalex.org/W1586623601","https://openalex.org/W1598074861","https://openalex.org/W1601908027","https://openalex.org/W1966300272","https://openalex.org/W1985787639","https://openalex.org/W1989060858","https://openalex.org/W1989665919","https://openalex.org/W1989703536","https://openalex.org/W1989819667","https://openalex.org/W1993077381","https://openalex.org/W2001012793","https://openalex.org/W2007751122","https://openalex.org/W2013950617","https://openalex.org/W2032842253","https://openalex.org/W2036333759","https://openalex.org/W2044959876","https://openalex.org/W2049473070","https://openalex.org/W2053695265","https://openalex.org/W2053931412","https://openalex.org/W2065874602","https://openalex.org/W2067267383","https://openalex.org/W2069048447","https://openalex.org/W2069961480","https://openalex.org/W2070753451","https://openalex.org/W2071557235","https://openalex.org/W2079222732","https://openalex.org/W2080416089","https://openalex.org/W2095507168","https://openalex.org/W2107813568","https://openalex.org/W2114612290","https://openalex.org/W2126165061","https://openalex.org/W2141969329","https://openalex.org/W2587075603","https://openalex.org/W3204708751","https://openalex.org/W4230110540","https://openalex.org/W4233226319","https://openalex.org/W4234972159","https://openalex.org/W4236120793","https://openalex.org/W4236858820","https://openalex.org/W4239829202","https://openalex.org/W4241042885","https://openalex.org/W4250470418","https://openalex.org/W4250831033","https://openalex.org/W4256036843","https://openalex.org/W4292166829","https://openalex.org/W4292519254","https://openalex.org/W6600212071","https://openalex.org/W6600708310","https://openalex.org/W6603593799","https://openalex.org/W6606572650","https://openalex.org/W6607475004","https://openalex.org/W6812912255","https://openalex.org/W6813427085","https://openalex.org/W6814802696"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2087496541","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2085564391","https://openalex.org/W1984758362","https://openalex.org/W2042049060","https://openalex.org/W2992936613","https://openalex.org/W2296389180"],"abstract_inverted_index":{"We":[0,79],"consider":[1],"finite":[2],"element":[3],"methods":[4],"for":[5],"a":[6,12,83,91,119],"model":[7],"second-order":[8],"elliptic":[9],"equation":[10],"on":[11,71,93],"general":[13,76],"bounded":[14],"convex":[15],"polygonal":[16],"or":[17],"polyhedral":[18],"domain.":[19],"Our":[20],"first":[21],"main":[22,113],"goal":[23],"is":[24,67,97,118],"to":[25,69,74],"extend":[26],"the":[27,32,35,94,102,122,135],"best":[28],"approximation":[29],"property":[30],"of":[31,115,121,124],"error":[33],"in":[34,108,134],"<inline-formula":[36],"content-type=\"math/mathml\">":[37],"<mml:math":[38],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39],"alttext=\"upper":[40],"W":[41],"Subscript":[42],"normal":[43],"infinity":[44],"Superscript":[45],"1\">":[46],"<mml:semantics>":[47],"<mml:msubsup>":[48],"<mml:mi>W</mml:mi>":[49],"<mml:mrow":[50],"class=\"MJX-TeXAtom-ORD\">":[51],"<mml:mi":[52],"mathvariant=\"normal\">":[53],"\u221e":[54],"</mml:mi>":[55],"</mml:mrow>":[56],"<mml:mn>1</mml:mn>":[57],"</mml:msubsup>":[58],"<mml:annotation":[59],"encoding=\"application/x-tex\">W^1_{\\infty":[60],"}</mml:annotation>":[61],"</mml:semantics>":[62],"</mml:math>":[63],"</inline-formula>":[64],"norm,":[65],"which":[66,96],"known":[68],"hold":[70],"quasi-uniform":[72],"meshes,":[73],"more":[75,99],"graded":[77],"meshes.":[78],"accomplish":[80],"it":[81],"by":[82],"novel":[84],"proof":[85],"technique.":[86],"This":[87],"result":[88],"holds":[89],"under":[90],"condition":[92,105],"grid":[95],"mildly":[98],"restrictive":[100],"than":[101],"shape":[103],"regularity":[104],"typically":[106],"enforced":[107],"adaptive":[109],"codes.":[110],"The":[111],"second":[112],"contribution":[114],"this":[116],"work":[117],"discussion":[120],"properties":[123],"and":[125],"relationships":[126],"between":[127],"similar":[128],"mesh":[129],"restrictions":[130],"that":[131],"have":[132],"appeared":[133],"literature.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}