{"id":"https://openalex.org/W4308001758","doi":"https://doi.org/10.1007/s00211-022-01324-w","title":"Error estimates for total-variation regularized minimization problems with singular dual solutions","display_name":"Error estimates for total-variation regularized minimization problems with singular dual solutions","publication_year":2022,"publication_date":"2022-11-01","ids":{"openalex":"https://openalex.org/W4308001758","doi":"https://doi.org/10.1007/s00211-022-01324-w"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-022-01324-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01324-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01324-w.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/s00211-022-01324-w.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":["Institute of Applied Mathematics, Albert\u2013Ludwigs\u2013University Freiburg, Hermann\u2013Herder\u2013Stra\u00dfe 10, 79104, Freiburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Albert\u2013Ludwigs\u2013University Freiburg, Hermann\u2013Herder\u2013Stra\u00dfe 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/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":true,"raw_author_name":"Alex Kaltenbach","raw_affiliation_strings":["Institute of Applied Mathematics, Albert\u2013Ludwigs\u2013University Freiburg, Ernst\u2013Zermelo\u2013Stra\u00dfe 1, 79104, Freiburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Albert\u2013Ludwigs\u2013University Freiburg, Ernst\u2013Zermelo\u2013Stra\u00dfe 1, 79104, Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071740124"],"corresponding_institution_ids":["https://openalex.org/I161046081"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6638,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62727962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"152","issue":"4","first_page":"881","last_page":"906"},"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":0.9997000098228455,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8846242427825928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8523565530776978},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.7055710554122925},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6730107665061951},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6265654563903809},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6201567053794861},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6119999289512634},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5968398451805115},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5729784965515137},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4924052953720093},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.42497074604034424},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38976722955703735},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3868342638015747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12013512849807739},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09966516494750977}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8846242427825928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8523565530776978},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.7055710554122925},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6730107665061951},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6265654563903809},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6201567053794861},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6119999289512634},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5968398451805115},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5729784965515137},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4924052953720093},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.42497074604034424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38976722955703735},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3868342638015747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12013512849807739},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09966516494750977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-022-01324-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01324-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01324-w.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-022-01324-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01324-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01324-w.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308001758.pdf","grobid_xml":"https://content.openalex.org/works/W4308001758.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W418503264","https://openalex.org/W592911714","https://openalex.org/W595086808","https://openalex.org/W1480714962","https://openalex.org/W1545761024","https://openalex.org/W1601728065","https://openalex.org/W1609275808","https://openalex.org/W1976688370","https://openalex.org/W1983814397","https://openalex.org/W1997003380","https://openalex.org/W2011301426","https://openalex.org/W2034511734","https://openalex.org/W2039939700","https://openalex.org/W2059450582","https://openalex.org/W2065383341","https://openalex.org/W2067736594","https://openalex.org/W2082608952","https://openalex.org/W2100533333","https://openalex.org/W2103559027","https://openalex.org/W2146785120","https://openalex.org/W2963279928","https://openalex.org/W2963777691","https://openalex.org/W3005256420","https://openalex.org/W3156205425","https://openalex.org/W3158123692","https://openalex.org/W3173996614","https://openalex.org/W3204708751","https://openalex.org/W4205815276","https://openalex.org/W4236384742"],"related_works":["https://openalex.org/W2073281382","https://openalex.org/W3014335474","https://openalex.org/W2897842840","https://openalex.org/W2022300732","https://openalex.org/W2040666836","https://openalex.org/W1516906190","https://openalex.org/W2499849978","https://openalex.org/W4293385557","https://openalex.org/W2238041693","https://openalex.org/W4226360335"],"abstract_inverted_index":{"Abstract":[0],"Recent":[1],"quasi-optimal":[2],"error":[3,60],"estimates":[4,61],"for":[5],"the":[6,16,20,39,52,66],"finite":[7],"element":[8,18],"approximation":[9],"of":[10,22,42,69],"total-variation":[11],"regularized":[12],"minimization":[13],"problems":[14],"using":[15],"Crouzeix\u2013Raviart":[17],"require":[19],"existence":[21],"a":[23,43,70],"Lipschitz":[24,40,53],"continuous":[25],"dual":[26,44,72],"solution,":[27],"which":[28],"is":[29,46],"not":[30,47],"generally":[31],"given.":[32],"We":[33],"provide":[34],"analytic":[35],"proofs":[36],"showing":[37],"that":[38,62],"continuity":[41],"solution":[45],"necessary,":[48],"in":[49,57],"general.":[50],"Using":[51],"truncation":[54],"technique,":[55],"we,":[56],"addition,":[58],"derive":[59],"depend":[63],"directly":[64],"on":[65],"Sobolev":[67],"regularity":[68],"given":[71],"solution.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}