{"id":"https://openalex.org/W1973664641","doi":"https://doi.org/10.1137/070708792","title":"A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems","display_name":"A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1973664641","doi":"https://doi.org/10.1137/070708792","mag":"1973664641"},"language":"en","primary_location":{"id":"doi:10.1137/070708792","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070708792","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0711.3928","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070767719","display_name":"Alan Demlow","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan Demlow","raw_affiliation_strings":["demlow@ms.uky.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"demlow@ms.uky.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072471752","display_name":"Omar Lakkis","orcid":"https://orcid.org/0000-0002-1339-1464"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omar Lakkis","raw_affiliation_strings":["o.lakkis@sussex.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"o.lakkis@sussex.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105693474","display_name":"Charalambos Makridakis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charalambos Makridakis","raw_affiliation_strings":["makr@tem.uoc.gr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"makr@tem.uoc.gr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8737,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.84432144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"47","issue":"3","first_page":"2157","last_page":"2176"},"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":0.9990000128746033,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8749055862426758},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6774317026138306},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6486949920654297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4768066108226776},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.46710196137428284},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.46613451838493347},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3783579468727112},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2341431975364685}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8749055862426758},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6774317026138306},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6486949920654297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4768066108226776},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.46710196137428284},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.46613451838493347},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3783579468727112},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2341431975364685},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/070708792","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070708792","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:arXiv.org:0711.3928","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0711.3928","pdf_url":"https://arxiv.org/pdf/0711.3928","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":"pmh:oai:CiteSeerX.psu:10.1.1.315.7712","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.315.7712","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/0711.3928v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.488.3234","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.488.3234","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/apost_par.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.494.2365","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.494.2365","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.sussex.ac.uk/preprints/document/SMRR-2007-04.pdf","raw_type":"text"},{"id":"pmh:oai:alma.39UBZ_INST:11293055310001241","is_oa":false,"landing_page_url":"http://arxiv.org/abs/0711.3928","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/23345489","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_Posteriori_Error_Estimates_in_the_Maximum_Norm_for_Parabolic_Problems/23345489","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:unibz.it:11293055310001241","is_oa":false,"landing_page_url":"https://bia.unibz.it/esploro/outputs/journalArticle/A-posteriori-error-estimates-in-the/991006493987401241","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0711.3928","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0711.3928","pdf_url":"https://arxiv.org/pdf/0711.3928","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":[],"awards":[{"id":"https://openalex.org/G985928306","display_name":"PostDoctoral Research Fellowship","funder_award_id":"0303378","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"},{"id":"https://openalex.org/F4320319997","display_name":"Nuffield Foundation","ror":"https://ror.org/0281jqk77"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W18246449","https://openalex.org/W24460554","https://openalex.org/W99776242","https://openalex.org/W591292934","https://openalex.org/W1488071155","https://openalex.org/W1989665919","https://openalex.org/W1993223059","https://openalex.org/W1996672299","https://openalex.org/W2002086758","https://openalex.org/W2011913964","https://openalex.org/W2030685662","https://openalex.org/W2038626747","https://openalex.org/W2044627846","https://openalex.org/W2047378168","https://openalex.org/W2048715903","https://openalex.org/W2069048447","https://openalex.org/W2074006304","https://openalex.org/W2079626492","https://openalex.org/W2082621526","https://openalex.org/W2101412448","https://openalex.org/W2114373425","https://openalex.org/W2115218270","https://openalex.org/W2126165061","https://openalex.org/W2429258439","https://openalex.org/W2593396912","https://openalex.org/W4205289336","https://openalex.org/W4250220742","https://openalex.org/W4250357529","https://openalex.org/W4250470418"],"related_works":["https://openalex.org/W2362625355","https://openalex.org/W2020718081","https://openalex.org/W2610540941","https://openalex.org/W4299447939","https://openalex.org/W2332908959","https://openalex.org/W3007553996","https://openalex.org/W3137869026","https://openalex.org/W2023658642","https://openalex.org/W2006902680","https://openalex.org/W2893622182"],"abstract_inverted_index":{"We":[0,51],"derive":[1],"a":[2,39,54,58],"posteriori":[3,40,55],"error":[4,88],"estimates":[5,31,82],"in":[6,42],"the":[7,19,43,76],"$L_\\infty((0,T];L_\\infty(\\Omega))$":[8],"norm":[9,45,87],"for":[10,32,46,57],"approximations":[11],"of":[12,79],"solutions":[13],"to":[14],"linear":[15,33],"parabolic":[16,34],"equations.":[17],"Using":[18],"elliptic":[20,67,85],"reconstruction":[21,68],"technique":[22,69],"introduced":[23],"by":[24,74],"Makridakis":[25],"and":[26,28],"Nochetto":[27],"heat":[29,80],"kernel":[30,81],"problems,":[35],"we":[36],"first":[37],"prove":[38],"bounds":[41,56],"maximum":[44,86],"semidiscrete":[47],"finite":[48,63],"element":[49,64],"approximations.":[50],"then":[52],"establish":[53],"fully":[59],"discrete":[60],"backward":[61],"Euler":[62],"approximation.":[65],"The":[66],"greatly":[70],"simplifies":[71],"our":[72],"development":[73],"allowing":[75],"straightforward":[77],"combination":[78],"with":[83],"existing":[84],"estimators.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
