{"id":"https://openalex.org/W2560438502","doi":"https://doi.org/10.1515/cmam-2017-0060","title":"An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations","display_name":"An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations","publication_year":2017,"publication_date":"2017-12-20","ids":{"openalex":"https://openalex.org/W2560438502","doi":"https://doi.org/10.1515/cmam-2017-0060","mag":"2560438502"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2017-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0060","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.01411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074373665","display_name":"Immanuel Anjam","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Immanuel Anjam","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Duisburg\u2013Essen , Campus Essen , Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Duisburg\u2013Essen , Campus Essen , Germany","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041687955","display_name":"Dirk Pauly","orcid":"https://orcid.org/0000-0003-4155-7297"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dirk Pauly","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Duisburg\u2013Essen , Campus Essen , Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Duisburg\u2013Essen , Campus Essen , Germany","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074373665"],"corresponding_institution_ids":["https://openalex.org/I62318514"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00650965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"2","first_page":"311","last_page":"322"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9954000115394592,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9948999881744385,"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.8156930208206177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7441813349723816},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6384327411651611},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5819885730743408},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5408085584640503},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5384547114372253},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5260184407234192},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4967373013496399},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.48269128799438477},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.341228723526001},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2820664048194885}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.8156930208206177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7441813349723816},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6384327411651611},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5819885730743408},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5408085584640503},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5384547114372253},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5260184407234192},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4967373013496399},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.48269128799438477},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.341228723526001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2820664048194885},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/cmam-2017-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0060","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.01411","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.01411","pdf_url":"https://arxiv.org/pdf/1612.01411","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2560438502","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1612.01411.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1612.01411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.01411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.01411","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.01411","pdf_url":"https://arxiv.org/pdf/1612.01411","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2560438502.pdf","grobid_xml":"https://content.openalex.org/works/W2560438502.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W408406386","https://openalex.org/W592911714","https://openalex.org/W599756203","https://openalex.org/W1521778258","https://openalex.org/W1583622322","https://openalex.org/W2493337726","https://openalex.org/W2963534781"],"related_works":["https://openalex.org/W2963390273","https://openalex.org/W2284045066","https://openalex.org/W2963150096","https://openalex.org/W1883936784","https://openalex.org/W2561792779","https://openalex.org/W2555609230","https://openalex.org/W3125303363","https://openalex.org/W2367196520","https://openalex.org/W1973359993","https://openalex.org/W3201702985","https://openalex.org/W2081625676","https://openalex.org/W1973089856","https://openalex.org/W2084132784","https://openalex.org/W2033160321","https://openalex.org/W2085721388","https://openalex.org/W2060745404","https://openalex.org/W2053266167","https://openalex.org/W2158710357","https://openalex.org/W190583845","https://openalex.org/W2093525003"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"present":[5],"a":[6,11,30],"simple":[7],"method":[8],"of":[9,59],"deriving":[10],"posteriori":[12],"error":[13,26],"equalities":[14],"and":[15,20,39,52,62],"estimates":[16],"for":[17],"linear":[18],"elliptic":[19],"parabolic":[21],"partial":[22],"differential":[23],"equations.":[24],"The":[25],"is":[27],"measured":[28],"in":[29],"combined":[31],"norm":[32],"taking":[33],"into":[34],"account":[35],"both":[36],"the":[37,46],"primal":[38],"dual":[40],"variables.":[41],"We":[42],"work":[43],"only":[44],"on":[45],"continuous":[47],"(often":[48],"called":[49],"functional)":[50],"level":[51],"do":[53],"not":[54],"suppose":[55],"any":[56],"specific":[57],"properties":[58],"numerical":[60],"methods":[61],"discretizations.":[63]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
