{"id":"https://openalex.org/W2003049157","doi":"https://doi.org/10.1137/s0036142903413002","title":"A Posteriori Error Estimates Based on the Polynomial Preserving Recovery","display_name":"A Posteriori Error Estimates Based on the Polynomial Preserving Recovery","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2003049157","doi":"https://doi.org/10.1137/s0036142903413002","mag":"2003049157"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903413002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903413002","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/A5049971564","display_name":"Ahmed Naga","orcid":null},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ahmed Naga","raw_affiliation_strings":["Wayne State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wayne State University","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100406520","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-0531-9112"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Wayne State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wayne State University","institution_ids":["https://openalex.org/I185443292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185443292"],"apc_list":null,"apc_paid":null,"fwci":6.6804,"has_fulltext":false,"cited_by_count":155,"citation_normalized_percentile":{"value":0.96900301,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"42","issue":"4","first_page":"1780","last_page":"1800"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9958999752998352,"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":0.9950000047683716,"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/superconvergence","display_name":"Superconvergence","score":0.9596409797668457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8559951186180115},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7175723314285278},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6810874342918396},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6573816537857056},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6020814776420593},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34843122959136963},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3213709592819214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27900147438049316},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15568146109580994}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9596409797668457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8559951186180115},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7175723314285278},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6810874342918396},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6573816537857056},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6020814776420593},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34843122959136963},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3213709592819214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27900147438049316},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15568146109580994},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142903413002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903413002","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:digitalcommons.wayne.edu:math_reports-1005","is_oa":false,"landing_page_url":"https://digitalcommons.wayne.edu/math_reports/6","pdf_url":null,"source":{"id":"https://openalex.org/S171990522","display_name":"Human Biology","issn_l":"0018-7143","issn":["0018-7143","1534-6617"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316469","host_organization_name":"Wayne State University Press","host_organization_lineage":["https://openalex.org/P4310316469"],"host_organization_lineage_names":["Wayne State University Press"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Research Reports","raw_type":"tech_report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.7626","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.7626","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.wayne.edu/~zzhang/paper/zhang-naga2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W306588069","https://openalex.org/W1595515622","https://openalex.org/W1964488237","https://openalex.org/W1980964769","https://openalex.org/W1994336408","https://openalex.org/W1995404822","https://openalex.org/W2024409565","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2050178911","https://openalex.org/W2061937382","https://openalex.org/W2065479689","https://openalex.org/W2071036364","https://openalex.org/W2122602456","https://openalex.org/W2155395549","https://openalex.org/W2157121531","https://openalex.org/W2163694039","https://openalex.org/W2171737318","https://openalex.org/W2505585705"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W2160252404","https://openalex.org/W4230524683","https://openalex.org/W3141012097","https://openalex.org/W2964478211","https://openalex.org/W3150274214","https://openalex.org/W3123431136"],"abstract_inverted_index":{"Abstract":[0],"Superconvergence":[1],"of":[2],"order":[3],"O(h":[4],"1+\u03c1),":[5],"for":[6,12],"some":[7],"\u03c1&amp;gt;":[8],"0,":[9],"is":[10,25],"established":[11],"the":[13,17,23,29],"gradient":[14,31],"recovered":[15],"with":[16],"Polynomial":[18],"Preserving":[19],"Recovery":[20],"(PPR)":[21],"when":[22],"mesh":[24],"mildly":[26],"structured.":[27],"Consequently,":[28],"PPR-recovered":[30],"can":[32],"be":[33],"used":[34],"in":[35],"building":[36],"an":[37],"asymptotically":[38],"exact":[39],"a":[40],"posteriori":[41],"error":[42],"estimator.":[43]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
