{"id":"https://openalex.org/W2007751122","doi":"https://doi.org/10.1090/s0025-5718-98-00959-4","title":"Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates","display_name":"Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2007751122","doi":"https://doi.org/10.1090/s0025-5718-98-00959-4","mag":"2007751122"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00959-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00959-4","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Alfred Schatz","raw_affiliation_strings":["Department of Mathematics, White Hall, Cornell University, Ithaca, New York 14853"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, White Hall, Cornell University, Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052440884"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":3.1962,"has_fulltext":true,"cited_by_count":115,"citation_normalized_percentile":{"value":0.90905161,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"67","issue":"223","first_page":"877","last_page":"899"},"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":0.9991000294685364,"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":0.9973000288009644,"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/algorithm","display_name":"Algorithm","score":0.6764800548553467},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6526191830635071},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.4331347942352295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40278205275535583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36754271388053894},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35778266191482544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12875312566757202}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6764800548553467},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6526191830635071},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.4331347942352295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40278205275535583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36754271388053894},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35778266191482544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12875312566757202}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-98-00959-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00959-4","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.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":null,"license_id":null,"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/s0025-5718-98-00959-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00959-4","pdf_url":"https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.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":null,"license_id":null,"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/G8475619926","display_name":"Mathematical Sciences: Algorithms and Numerical Analysis    for Partial Differential Equations","funder_award_id":"9403512","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/W2007751122.pdf","grobid_xml":"https://content.openalex.org/works/W2007751122.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W105661347","https://openalex.org/W410026136","https://openalex.org/W1866311589","https://openalex.org/W1955535265","https://openalex.org/W1989819667","https://openalex.org/W2001012793","https://openalex.org/W2005601391","https://openalex.org/W2023868969","https://openalex.org/W2061937382","https://openalex.org/W2065279412","https://openalex.org/W2065874602","https://openalex.org/W2095167396","https://openalex.org/W4233226319","https://openalex.org/W4234694874","https://openalex.org/W4236381143","https://openalex.org/W4241042885"],"related_works":["https://openalex.org/W2140020064","https://openalex.org/W143502885","https://openalex.org/W42113618","https://openalex.org/W2103468410","https://openalex.org/W1856228368","https://openalex.org/W3197542402","https://openalex.org/W2361861616","https://openalex.org/W2971527398","https://openalex.org/W1025150868","https://openalex.org/W2645958880"],"abstract_inverted_index":{"This":[0],"part":[1],"contains":[2],"new":[3,189],"pointwise":[4],"error":[5,126,141,192],"estimates":[6,123,188,267],"for":[7,12,124,209],"the":[8,125,140,146,149,169,200],"finite":[9,172,213],"element":[10,173],"method":[11],"second":[13],"order":[14,171,181],"elliptic":[15],"boundary":[16],"value":[17],"problems":[18],"on":[19,127,145,216],"smooth":[20],"bounded":[21],"domains":[22],"in":[23,131,167,199,219],"<inline-formula":[24,64,91,151,220],"content-type=\"math/mathml\">":[25,65,92,152,221],"<mml:math":[26,66,93,153,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[27,67,94,154,223],"alttext=\"double-struck":[28,224],"upper":[29,32,225,228],"R":[30,226],"Superscript":[31,100,227],"N\">":[33,229],"<mml:semantics>":[34,73,102,156,230],"<mml:msup>":[35,231],"<mml:mrow":[36,41,76,105,112,232,237],"class=\"MJX-TeXAtom-ORD\">":[37,42,77,106,113,233,238],"<mml:mi":[38,78,107,234],"mathvariant=\"double-struck\">R</mml:mi>":[39,235],"</mml:mrow>":[40,44,82,111,115,236,240],"<mml:mi>N</mml:mi>":[43,239],"</mml:msup>":[45,241],"<mml:annotation":[46,84,117,158,242],"encoding=\"application/x-tex\">\\mathbb":[47,243],"{R}^{N}</mml:annotation>":[48,244],"</mml:semantics>":[49,87,120,160,245],"</mml:math>":[50,88,121,161,246],"</inline-formula>":[51,89,122,162,247],".":[52,163],"In":[53],"a":[54,135,143,184,256],"sense":[55],"to":[56,251,269],"be":[57,195],"discussed":[58],"below":[59],"these":[60,187],"sharpen":[61],"known":[62],"quasi\u2013optimal":[63],"alttext=\"upper":[68,95],"L":[69],"Subscript":[70,97],"normal":[71,98],"infinity\">":[72],"<mml:msub>":[74],"<mml:mi>L</mml:mi>":[75],"mathvariant=\"normal\">":[79,108],"\u221e":[80,109],"</mml:mi>":[81,110],"</mml:msub>":[83],"encoding=\"application/x-tex\">L_{\\infty":[85],"}</mml:annotation>":[86,119],"and":[90,248,253,255],"W":[96],"infinity":[99],"1\">":[101],"<mml:msubsup>":[103],"<mml:mi>W</mml:mi>":[104],"<mml:mn>1</mml:mn>":[114],"</mml:msubsup>":[116],"encoding=\"application/x-tex\">W^{1}_{\\infty":[118],"irregular":[128,217],"quasi\u2013uniform":[129],"meshes":[130],"that":[132,166],"they":[133],"indicate":[134],"more":[136,176],"local":[137,177,266],"dependence":[138],"of":[139,148,186,191,202,212,261],"at":[142],"point":[144],"derivatives":[147],"solution":[150],"alttext=\"u\">":[155],"<mml:mi>u</mml:mi>":[157],"encoding=\"application/x-tex\">u</mml:annotation>":[159],"We":[164],"note":[165],"general":[168],"higher":[170],"spaces":[174],"exhibit":[175],"behavior":[178],"than":[179],"lower":[180],"spaces.":[182],"As":[183],"consequence":[185],"types":[190],"expansions":[193],"will":[194,264],"derived":[196],"which":[197],"are":[198,207],"form":[201],"inequalities.":[203],"These":[204],"expansion":[205],"inequalities":[206],"valid":[208],"large":[210],"classes":[211],"elements":[214],"defined":[215],"grids":[218],"have":[249],"applications":[250],"superconvergence":[252],"extrapolation":[254],"posteriori":[257],"estimates.":[258],"Part":[259],"II":[260],"this":[262],"series":[263],"contain":[265],"applicable":[268],"non\u2013smooth":[270],"problems.":[271]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}