{"id":"https://openalex.org/W2087750281","doi":"https://doi.org/10.1137/s0036142902408131","title":"Perturbations of Forms and Error Estimates for the Finite Element Method at a Point, with an Application to Improved Superconvergence Error Estimates for Subspaces that Are Symmetric with Respect to a Point","display_name":"Perturbations of Forms and Error Estimates for the Finite Element Method at a Point, with an Application to Improved Superconvergence Error Estimates for Subspaces that Are Symmetric with Respect to a Point","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2087750281","doi":"https://doi.org/10.1137/s0036142902408131","mag":"2087750281"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902408131","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902408131","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052440884","display_name":"A. H. Schatz","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alfred H. Schatz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5052440884"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6569,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83430222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"6","first_page":"2342","last_page":"2365"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.9229018688201904},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8737152814865112},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8378204107284546},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5531394481658936},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5441556572914124},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.472536563873291},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4721774458885193},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46719691157341003},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.43856093287467957},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4033171534538269},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2952682375907898},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0975261926651001},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06946226954460144}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9229018688201904},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8737152814865112},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8378204107284546},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5531394481658936},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5441556572914124},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.472536563873291},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4721774458885193},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46719691157341003},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.43856093287467957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4033171534538269},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2952682375907898},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0975261926651001},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06946226954460144},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142902408131","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902408131","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W50503297","https://openalex.org/W410026136","https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1595515622","https://openalex.org/W1989819667","https://openalex.org/W2001012793","https://openalex.org/W2005601391","https://openalex.org/W2006453627","https://openalex.org/W2007751122","https://openalex.org/W2046573877","https://openalex.org/W2064682864","https://openalex.org/W2065874602","https://openalex.org/W2107934709","https://openalex.org/W4252219741"],"related_works":["https://openalex.org/W2355289483","https://openalex.org/W4389426186","https://openalex.org/W2385047956","https://openalex.org/W2385959805","https://openalex.org/W2370072269","https://openalex.org/W2964478211","https://openalex.org/W4200053212","https://openalex.org/W4200516922","https://openalex.org/W2235548299","https://openalex.org/W2197675418"],"abstract_inverted_index":{"We":[0,101],"first":[1],"derive":[2],"a":[3,14,22,49],"variety":[4],"of":[5,51,84],"local":[6,35],"error":[7,109],"estimates":[8,110],"for":[9,40],"u":[10,32],"-":[11],"uh":[12,19],"at":[13,125],"point":[15],"x0":[16,52,127,136],",":[17],"where":[18,128],"belongs":[20],"to":[21,31,105,135],"finite":[23],"element":[24],"space":[25],"Shr":[26,44],"and":[27,66,115],"is":[28],"an":[29],"approximation":[30],"satisfying":[33],"the":[34,55,67,73,107,129],"equations":[36,65],"$A(u-u_h,\\varphi)":[37],"=":[38],"F(\\varphi)$":[39],"all":[41],"$\\varphi$":[42],"in":[43,48],"with":[45,61,82,133],"compact":[46],"support":[47],"neighborhood":[50],".":[53,137],"Here":[54],"$A(\\cdot,\\cdot)$":[56],"are":[57,69,95,131],"bilinear":[58],"forms":[59],"associated":[60],"second":[62],"order":[63],"elliptic":[64],"F":[68],"linear":[70],"functionals.":[71],"In":[72],"case":[74],"that":[75],"$F":[76,98],"\\equiv":[77],"0$":[78],"our":[79],"results":[80,104],"coincide":[81],"those":[83],"Schatz":[85],"[SIAM":[86,117],"J.":[87,118],"Numer.":[88,119],"Anal.,":[89,120],"38":[90],"(2000),":[91],"pp.":[92,123],"1269--1293]":[93],"but":[94],"improvements":[96],"when":[97],"\\neq":[99],"0$.":[100],"apply":[102],"these":[103],"improve":[106],"superconvergence":[108],"obtained":[111],"by":[112],"Schatz,":[113],"Sloan,":[114],"Wahlbin":[116],"33":[121],"(1996),":[122],"505--521]":[124],"points":[126],"subspaces":[130],"symmetric":[132],"respect":[134]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
