{"id":"https://openalex.org/W2071557235","doi":"https://doi.org/10.1090/s0025-5718-2010-02353-1","title":"Local energy estimates for the finite element method on sharply varying grids","display_name":"Local energy estimates for the finite element method on sharply varying grids","publication_year":2010,"publication_date":"2010-06-28","ids":{"openalex":"https://openalex.org/W2071557235","doi":"https://doi.org/10.1090/s0025-5718-2010-02353-1","mag":"2071557235"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2010-02353-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02353-1","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02353-1/S0025-5718-2010-02353-1.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/2011-80-273/S0025-5718-2010-02353-1/S0025-5718-2010-02353-1.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":"Alan Demlow","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506\u00e2\u0080\u00930027","Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506\u20130027"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506\u00e2\u0080\u00930027","institution_ids":["https://openalex.org/I143302722"]},{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506\u20130027","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036599010","display_name":"Johnny Guzm\u00e1n","orcid":"https://orcid.org/0000-0002-6769-2393"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Johnny Guzm\u00e1n","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02906"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02906","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","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":"Alfred Schatz","raw_affiliation_strings":["Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1155,"has_fulltext":true,"cited_by_count":58,"citation_normalized_percentile":{"value":0.87233129,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"80","issue":"273","first_page":"1","last_page":"9"},"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":1.0,"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":1.0,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.998199999332428,"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":0.7803226709365845},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7491484880447388},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6824765801429749},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6675103306770325},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6672776937484741},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5849617719650269},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5763493776321411},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5265108346939087},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48567378520965576},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4029596149921417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32537946105003357},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2353336215019226},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1045944094657898}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803226709365845},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7491484880447388},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6824765801429749},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6675103306770325},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6672776937484741},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5849617719650269},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5763493776321411},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5265108346939087},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48567378520965576},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4029596149921417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32537946105003357},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2353336215019226},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1045944094657898},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-2010-02353-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02353-1","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02353-1/S0025-5718-2010-02353-1.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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.6061","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.6061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0808.2160v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.524.2742","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.524.2742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dam.brown.edu/people/jguzman/preprints/gAlan.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.538.6470","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.538.6470","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ms.uky.edu/~demlow/pubs/localhone.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2010-02353-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02353-1","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02353-1/S0025-5718-2010-02353-1.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":[],"awards":[{"id":"https://openalex.org/G4710313902","display_name":"PostDoctoral Research Fellowship","funder_award_id":"0503050","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"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"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071557235.pdf","grobid_xml":"https://content.openalex.org/works/W2071557235.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W829592196","https://openalex.org/W1492326914","https://openalex.org/W1522425331","https://openalex.org/W1776589346","https://openalex.org/W1963512446","https://openalex.org/W1989819667","https://openalex.org/W1993779177","https://openalex.org/W1995751822","https://openalex.org/W2001012793","https://openalex.org/W2069961480","https://openalex.org/W2070753451","https://openalex.org/W2079626492","https://openalex.org/W2079883859","https://openalex.org/W2114373425","https://openalex.org/W2133147107","https://openalex.org/W4241042885","https://openalex.org/W4252219741"],"related_works":["https://openalex.org/W2163017860","https://openalex.org/W1850281117","https://openalex.org/W4294364856","https://openalex.org/W2164522043","https://openalex.org/W2315570462","https://openalex.org/W2155632758","https://openalex.org/W2299552569","https://openalex.org/W4383216082","https://openalex.org/W4377164417","https://openalex.org/W2163912400"],"abstract_inverted_index":{"Local":[0],"energy":[1,27,79],"error":[2,28],"estimates":[3,22,80],"for":[4,9,92],"the":[5,25,44,51,62,102],"finite":[6],"element":[7],"method":[8],"elliptic":[10],"problems":[11],"were":[12],"originally":[13],"proved":[14],"in":[15],"1974":[16],"by":[17,32],"Nitsche":[18,66],"and":[19,55,67,96],"Schatz.":[20],"These":[21],"show":[23],"that":[24,42,81],"local":[26,34,76],"may":[29],"be":[30],"bounded":[31],"a":[33,38,77],"approximation":[35],"term,":[36],"plus":[37],"global":[39],"\u201cpollution\u201d":[40],"term":[41],"measures":[43],"influence":[45],"of":[46,53,58,65],"solution":[47],"quality":[48],"from":[49],"outside":[50],"domain":[52],"interest":[54],"is":[56,69,110],"heuristically":[57],"higher":[59],"order.":[60],"However,":[61],"original":[63],"analysis":[64],"Schatz":[68],"restricted":[70],"to":[71],"quasi-uniform":[72],"grids.":[73],"We":[74],"present":[75],"priori":[78],"are":[82],"valid":[83],"on":[84],"shape":[85],"regular":[86],"grids,":[87],"an":[88,111],"assumption":[89],"which":[90,97],"allows":[91],"highly":[93],"graded":[94],"meshes":[95],"matches":[98],"much":[99],"more":[100],"closely":[101],"typical":[103],"practical":[104],"situation.":[105],"Our":[106],"chief":[107],"technical":[108],"innovation":[109],"improved":[112],"superapproximation":[113],"result.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
