{"id":"https://openalex.org/W2053099075","doi":"https://doi.org/10.1137/100782760","title":"An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems","display_name":"An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2053099075","doi":"https://doi.org/10.1137/100782760","mag":"2053099075"},"language":"en","primary_location":{"id":"doi:10.1137/100782760","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100782760","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/A5023761859","display_name":"Sajid Memon","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sajid Memon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019365126","display_name":"Neela Nataraj","orcid":"https://orcid.org/0000-0002-5180-459X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neela Nataraj","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034307785","display_name":"Amiya K. Pani","orcid":"https://orcid.org/0000-0002-0477-9272"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amiya Kumar Pani","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023761859"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0286,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.76245802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"50","issue":"3","first_page":"1367","last_page":"1393"},"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/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/T10514","display_name":"Numerical methods in engineering","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.8520349264144897},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7471134066581726},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7388492226600647},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6411323547363281},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6404436826705933},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6229356527328491},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5768215656280518},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4962652325630188},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4691820442676544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4383035898208618},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.2596345543861389},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06510135531425476}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8520349264144897},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7471134066581726},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7388492226600647},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6411323547363281},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6404436826705933},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6229356527328491},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5768215656280518},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4962652325630188},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4691820442676544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4383035898208618},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.2596345543861389},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06510135531425476},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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:10.1137/100782760","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100782760","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:repository.kaust.edu.sa:10754/597504","is_oa":false,"landing_page_url":"http://repository.kaust.edu.sa/kaust/handle/10754/597504","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/15195","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/jspui/handle/100/15195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W21480455","https://openalex.org/W1973664641","https://openalex.org/W1980883473","https://openalex.org/W1993064848","https://openalex.org/W2006443697","https://openalex.org/W2024326406","https://openalex.org/W2030054511","https://openalex.org/W2030685662","https://openalex.org/W2038626747","https://openalex.org/W2047378168","https://openalex.org/W2056027508","https://openalex.org/W2063899632","https://openalex.org/W2064265943","https://openalex.org/W2064416388","https://openalex.org/W2067951086","https://openalex.org/W2068432368","https://openalex.org/W2074006304","https://openalex.org/W2081431069","https://openalex.org/W2156618899","https://openalex.org/W2808511068"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W4287880334","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W2377834777","https://openalex.org/W4390271665","https://openalex.org/W1965469317","https://openalex.org/W2069866412"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"a":[3,29,54,58,65,77],"posteriori":[4,30,66,78],"error":[5,31,67],"estimates":[6,32,79],"are":[7,45,69],"derived":[8],"for":[9,37,47],"mixed":[10,26,81],"finite":[11,82],"element":[12,83],"Galerkin":[13],"approximations":[14,84],"to":[15,85],"second":[16],"order":[17],"linear":[18],"parabolic":[19,86],"initial":[20],"and":[21,35,64],"boundary":[22],"value":[23],"problems.":[24,87],"Using":[25],"elliptic":[27],"reconstructions,":[28],"in":[33],"$L^{\\infty}(L^2)$-":[34],"$L^2(L^2)$-norms":[36],"the":[38,48,93,96],"solution":[39],"as":[40,42],"well":[41],"its":[43],"flux":[44],"proved":[46],"semidiscrete":[49],"scheme.":[50],"Finally,":[51],"based":[52],"on":[53,76],"backward":[55],"Euler":[56],"method,":[57],"completely":[59],"discrete":[60],"scheme":[61],"is":[62],"analyzed":[63],"bounds":[68],"derived,":[70],"which":[71],"improves":[72],"upon":[73],"earlier":[74],"results":[75],"of":[80,89,95],"Results":[88],"numerical":[90],"experiments":[91],"verifying":[92],"efficiency":[94],"estimators":[97],"have":[98],"also":[99],"been":[100],"provided.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}