{"id":"https://openalex.org/W1975208179","doi":"https://doi.org/10.1137/050641533","title":"Two\u2010Sided A Posteriori Error Estimates for Mixed Formulations of Elliptic Problems","display_name":"Two\u2010Sided A Posteriori Error Estimates for Mixed Formulations of Elliptic Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1975208179","doi":"https://doi.org/10.1137/050641533","mag":"1975208179"},"language":"en","primary_location":{"id":"doi:10.1137/050641533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641533","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113979788","display_name":"Sergey Repin","orcid":null},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Sergey Repin","raw_affiliation_strings":["Russian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Russian Academy of Sciences","institution_ids":["https://openalex.org/I1313323035"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049235940","display_name":"Stefan Sauter","orcid":"https://orcid.org/0000-0002-1403-1874"},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CH","CZ"],"is_corresponding":false,"raw_author_name":"Stefan Sauter","raw_affiliation_strings":["Institute of Mathematics, Zurich University, Winterthurerstrasse 190, CH-8057 Zurich, Switzer-land"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zurich University, Winterthurerstrasse 190, CH-8057 Zurich, Switzer-land","institution_ids":["https://openalex.org/I202697423","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000612435","display_name":"Anton Smolianski","orcid":null},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["BG","CH","CZ"],"is_corresponding":false,"raw_author_name":"Anton Smolianski","raw_affiliation_strings":["Institute of Mathematics, Zurich University, Winterthurerstrasse 190, CH-8057 Zurich, Switzer-land"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zurich University, Winterthurerstrasse 190, CH-8057 Zurich, Switzer-land","institution_ids":["https://openalex.org/I202697423","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113979788"],"corresponding_institution_ids":["https://openalex.org/I1313323035"],"apc_list":null,"apc_paid":null,"fwci":2.9993,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.89746721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"45","issue":"3","first_page":"928","last_page":"945"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8650614023208618},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7042068243026733},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5786669850349426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5667738914489746},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.5188085436820984},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4998161792755127},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4800454378128052},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.46343666315078735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3477743864059448},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12660038471221924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8650614023208618},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7042068243026733},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5786669850349426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5667738914489746},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.5188085436820984},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4998161792755127},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4800454378128052},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.46343666315078735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3477743864059448},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12660038471221924},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":4,"locations":[{"id":"doi:10.1137/050641533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641533","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:www.zora.uzh.ch:21574","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Repin, S; Sauter, S; Smolianski, A  (2007). Two-sided a posteriori error estimates for mixed formulations of elliptic problems.  SIAM Journal on Numerical Analysis, 45(3):928-945.","raw_type":"info:eu-repo/semantics/acceptedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.361.8394","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.8394","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uzh.ch/fileadmin/math/preprints/21-05.pdf","raw_type":"text"},{"id":"doi:10.5167/uzh-21574","is_oa":true,"landing_page_url":"https://doi.org/10.5167/uzh-21574","pdf_url":null,"source":{"id":"https://openalex.org/S7407051291","display_name":"Universit\u00e4t Z\u00fcrich, ZORA","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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-journal"}],"best_oa_location":{"id":"pmh:oai:www.zora.uzh.ch:21574","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Repin, S; Sauter, S; Smolianski, A  (2007). Two-sided a posteriori error estimates for mixed formulations of elliptic problems.  SIAM Journal on Numerical Analysis, 45(3):928-945.","raw_type":"info:eu-repo/semantics/acceptedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W46603733","https://openalex.org/W1514427379","https://openalex.org/W1607719246","https://openalex.org/W1653619892","https://openalex.org/W1674659126","https://openalex.org/W1852082788","https://openalex.org/W1966388474","https://openalex.org/W1989594010","https://openalex.org/W1993064848","https://openalex.org/W1998439772","https://openalex.org/W1998674934","https://openalex.org/W2024326406","https://openalex.org/W2029348449","https://openalex.org/W2034081303","https://openalex.org/W2036382499","https://openalex.org/W2037836476","https://openalex.org/W2041071536","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2048108115","https://openalex.org/W2059465899","https://openalex.org/W2075887353","https://openalex.org/W2079232547","https://openalex.org/W2082334670","https://openalex.org/W2088175558","https://openalex.org/W2094875449","https://openalex.org/W2132292023","https://openalex.org/W2143319269","https://openalex.org/W2146115533","https://openalex.org/W2155395549","https://openalex.org/W2166941505","https://openalex.org/W2171584351","https://openalex.org/W2562668947","https://openalex.org/W2996832619","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2954004777","https://openalex.org/W2949638731","https://openalex.org/W2951102138","https://openalex.org/W2362625355"],"abstract_inverted_index":{"The":[0,68,117,134],"present":[1],"work":[2],"is":[3,86],"devoted":[4],"to":[5],"the":[6,26,30,49,63,77,81,94,97,99,102,108,111,122,127,146,149,155,161],"a":[7],"posteriori":[8],"error":[9,27,109,151],"estimation":[10],"for":[11,25,43,58,107,145],"mixed":[12,124],"approximations":[13],"of":[14,48,65,93,101,120,129,148,163],"linear":[15,164],"self\u2010adjoint":[16],"elliptic":[17],"problems.":[18],"New":[19],"guaranteed":[20],"upper":[21,39,103],"and":[22,36,56,80,96,104,140],"lower":[23,105],"bounds":[24,40,106],"measured":[28],"in":[29,46,110,126],"natural":[31],"product":[32,112],"norm":[33,113],"are":[34,41,54,132,136,166],"derived,":[35],"individual":[37],"sharp":[38],"obtained":[42],"approximation":[44],"errors":[45],"each":[47],"physical":[50],"variables.":[51],"All":[52],"estimates":[53,69,135],"reliable":[55],"valid":[57],"any":[59],"approximate":[60,123],"solution":[61,125],"from":[62],"class":[64,128],"admissible":[66,130],"functions.":[67],"contain":[70],"only":[71],"global":[72],"constants":[73],"depending":[74],"solely":[75],"on":[76],"domain":[78],"geometry":[79],"given":[82],"operators.":[83],"Moreover,":[84],"it":[85],"shown":[87],"that,":[88],"after":[89],"an":[90],"appropriate":[91],"scaling":[92],"coordinates":[95],"equation,":[98],"ratio":[100],"never":[114],"exceeds":[115],"3.":[116],"possible":[118],"methods":[119],"finding":[121],"functions":[131],"discussed.":[133],"computationally":[137],"very":[138],"cheap":[139],"can":[141],"also":[142],"be":[143],"used":[144],"indication":[147],"local":[150],"distribution.":[152],"As":[153],"applications,":[154],"diffusion":[156],"problem":[157,162],"as":[158,160],"well":[159],"elasticity":[165],"considered.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
