{"id":"https://openalex.org/W4403535858","doi":"https://doi.org/10.1007/s10208-024-09676-5","title":"Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization","display_name":"Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization","publication_year":2024,"publication_date":"2024-10-18","ids":{"openalex":"https://openalex.org/W4403535858","doi":"https://doi.org/10.1007/s10208-024-09676-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-024-09676-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09676-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09676-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09676-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017359935","display_name":"S\u00f6ren Bartels","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S\u00f6ren Bartels","raw_affiliation_strings":["Department of Applied Mathematics, University of Freiburg, Hermann\u2013Herder\u2013Str. 10, 79104, Freiburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Freiburg, Hermann\u2013Herder\u2013Str. 10, 79104, Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071740124","display_name":"Alex Kaltenbach","orcid":"https://orcid.org/0000-0001-6478-7963"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alex Kaltenbach","raw_affiliation_strings":["Institute of Mathematics, Technical University of Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technical University of Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071740124"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.5146,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56620692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"26","issue":"1","first_page":"131","last_page":"177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9975000023841858,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9975000023841858,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9968000054359436,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematics","display_name":"Mathematics","score":0.7290360927581787},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6997565627098083},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6780684590339661},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.5591657161712646},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5361682176589966},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.5067735314369202},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4768470525741577},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4693770408630371},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46618956327438354},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41000449657440186},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36229273676872253},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3366889953613281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16314586997032166}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7290360927581787},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6997565627098083},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6780684590339661},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.5591657161712646},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5361682176589966},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.5067735314369202},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4768470525741577},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4693770408630371},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46618956327438354},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41000449657440186},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36229273676872253},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3366889953613281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16314586997032166},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-024-09676-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09676-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09676-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:264056","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bsz:25-freidok-2640564","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of computational mathematics. - 26, 1 (2026) , 131-177, ISSN: 1615-3383","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10208-024-09676-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09676-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09676-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403535858.pdf","grobid_xml":"https://content.openalex.org/works/W4403535858.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W253824085","https://openalex.org/W418503264","https://openalex.org/W1964524533","https://openalex.org/W1970610330","https://openalex.org/W1993004668","https://openalex.org/W1995536962","https://openalex.org/W2011181254","https://openalex.org/W2011301426","https://openalex.org/W2014307425","https://openalex.org/W2023040159","https://openalex.org/W2033468335","https://openalex.org/W2034511734","https://openalex.org/W2037868675","https://openalex.org/W2039924562","https://openalex.org/W2061988259","https://openalex.org/W2065383341","https://openalex.org/W2067736594","https://openalex.org/W2068432368","https://openalex.org/W2069697314","https://openalex.org/W2071552456","https://openalex.org/W2103559027","https://openalex.org/W2107813568","https://openalex.org/W2121179843","https://openalex.org/W2128095813","https://openalex.org/W2505585705","https://openalex.org/W2562668947","https://openalex.org/W2592623476","https://openalex.org/W2773019553","https://openalex.org/W2963279928","https://openalex.org/W3005256420","https://openalex.org/W3008959611","https://openalex.org/W3046527748","https://openalex.org/W3158123692","https://openalex.org/W3162868956","https://openalex.org/W3173996614","https://openalex.org/W3205128529","https://openalex.org/W4205815276","https://openalex.org/W4229650096","https://openalex.org/W4248049412","https://openalex.org/W4251401614","https://openalex.org/W4293874319","https://openalex.org/W4301021743","https://openalex.org/W4308001758","https://openalex.org/W4313495422","https://openalex.org/W4319323586","https://openalex.org/W4321643070","https://openalex.org/W6931794715"],"related_works":["https://openalex.org/W2142789187","https://openalex.org/W1561544985","https://openalex.org/W1992673508","https://openalex.org/W2116234265","https://openalex.org/W2075980626","https://openalex.org/W2037516588","https://openalex.org/W2126858039","https://openalex.org/W4249083923","https://openalex.org/W256114436","https://openalex.org/W1999876626"],"abstract_inverted_index":{"Abstract":[0],"In":[1,80],"this":[2],"paper,":[3],"we":[4,82],"propose":[5],"a":[6,11,39,57,63,75,84,90,97,119],"general":[7],"approach":[8],"for":[9,15],"explicit":[10,62],"posteriori":[12,64],"error":[13,65],"representation":[14,66],"convex":[16,21,51],"minimization":[17],"problems":[18],"using":[19],"basic":[20],"duality":[22,52],"relations.":[23],"Exploiting":[24],"discrete":[25,40,58,91,99],"orthogonality":[26],"relations":[27,53],"in":[28,94],"the":[29,44,47,61,108],"space":[30],"of":[31,78,96],"element-wise":[32],"constant":[33],"vector":[34],"fields":[35],"as":[36,38],"well":[37],"integration-by-parts":[41],"formula":[42,87],"between":[43],"Crouzeix\u2013Raviart":[45],"and":[46],"Raviart\u2013Thomas":[48],"element,":[49],"all":[50,104],"are":[54],"transferred":[55],"to":[56,113],"level,":[59],"making":[60],"\u2013initially":[67],"based":[68],"on":[69],"continuous":[70],"arguments":[71],"only\u2013":[72],"practicable":[73],"from":[74],"numerical":[76],"point":[77],"view.":[79],"addition,":[81],"provide":[83],"generalized":[85],"Marini":[86],"that":[88,117],"determines":[89],"primal":[92],"solution":[93],"terms":[95],"given":[98],"dual":[100],"solution.":[101],"We":[102],"benchmark":[103],"these":[105],"concepts":[106],"via":[107],"Rudin\u2013Osher\u2013Fatemi":[109],"model.":[110],"This":[111],"leads":[112],"an":[114],"adaptive":[115],"algorithm":[116],"yields":[118],"(quasi-optimal)":[120],"linear":[121],"convergence":[122],"rate.":[123]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
