{"id":"https://openalex.org/W1988307074","doi":"https://doi.org/10.1137/120901544","title":"Discrete Total Variation Flows without Regularization","display_name":"Discrete Total Variation Flows without Regularization","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1988307074","doi":"https://doi.org/10.1137/120901544","mag":"1988307074"},"language":"en","primary_location":{"id":"doi:10.1137/120901544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120901544","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/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":["Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg Hermann-Herder-Str. 10 79104 Freiburg i.Br., Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg Hermann-Herder-Str. 10 79104 Freiburg i.Br., Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028288239","display_name":"Abner J. Salgado","orcid":"https://orcid.org/0000-0002-3693-2104"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abner J. Salgado","raw_affiliation_strings":["Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA","Department of Mathematics, University of Maryland, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of Mathematics, University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028288239"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":2.7931,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.90175267,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"1","first_page":"363","last_page":"385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976999759674072,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9970999956130981,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9952999949455261,"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/regularization","display_name":"Regularization (linguistics)","score":0.8183584213256836},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.7797894477844238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7496378421783447},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.640282928943634},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5945526361465454},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.5634614825248718},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5597248673439026},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.46283650398254395},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44701966643333435},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4334973096847534},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.41232746839523315},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.23360171914100647},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21977707743644714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20270416140556335},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.1386854648590088},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0916266143321991},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06816193461418152}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.8183584213256836},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7797894477844238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7496378421783447},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.640282928943634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5945526361465454},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.5634614825248718},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5597248673439026},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.46283650398254395},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44701966643333435},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4334973096847534},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.41232746839523315},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.23360171914100647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21977707743644714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20270416140556335},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.1386854648590088},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0916266143321991},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06816193461418152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120901544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120901544","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1982444883","display_name":null,"funder_award_id":"DMS-1109325","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G432134336","display_name":"Adaptive Finite Element Methods for Multiscale Geometric PDE: Modeling, Analysis, and Computation","funder_award_id":"1109325","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4829642026","display_name":"Nonlinear Problems of Solid Mechanics","funder_award_id":"1008058","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6990594587","display_name":"Adaptive Finite Element Methods for Multiscale Problems Governed by Geometric PDE","funder_award_id":"0807811","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1970734370","https://openalex.org/W1976688370","https://openalex.org/W1980939071","https://openalex.org/W1993917000","https://openalex.org/W2020212762","https://openalex.org/W2022088322","https://openalex.org/W2026843256","https://openalex.org/W2031312034","https://openalex.org/W2034511734","https://openalex.org/W2043380148","https://openalex.org/W2045452373","https://openalex.org/W2057958367","https://openalex.org/W2068432368","https://openalex.org/W2071011575","https://openalex.org/W2079516848","https://openalex.org/W2087483865","https://openalex.org/W2088920136","https://openalex.org/W2089231054","https://openalex.org/W2092663520","https://openalex.org/W2100134371","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2105880637","https://openalex.org/W2132382511","https://openalex.org/W2137864075","https://openalex.org/W2166917874"],"related_works":["https://openalex.org/W2588406281","https://openalex.org/W2344001031","https://openalex.org/W1605636162","https://openalex.org/W2756378021","https://openalex.org/W4292601995","https://openalex.org/W2890366747","https://openalex.org/W4297923868","https://openalex.org/W3042163361","https://openalex.org/W2611470343","https://openalex.org/W2037789795"],"abstract_inverted_index":{"We":[0,40,64],"propose":[1,41],"and":[2,57,79],"analyze":[3],"an":[4,42],"algorithm":[5,19],"for":[6,45,62],"the":[7,10,14,24,28,46,49,54,70,73,76],"solution":[8,26,47,77],"of":[9,13,38,48,72],"$L^2$-subgradient":[11],"flow":[12],"total":[15],"variation":[16],"functional.":[17],"The":[18],"involves":[20],"no":[21],"regularization,":[22],"thus":[23],"numerical":[25,66],"preserves":[27],"main":[29],"features":[30],"that":[31,53],"motivate":[32],"practitioners":[33],"to":[34],"consider":[35],"this":[36],"type":[37],"energy.":[39],"iterative":[43],"scheme":[44],"arising":[50],"problems,":[51],"show":[52],"iterations":[55],"converge,":[56],"develop":[58],"a":[59],"stopping":[60],"criterion":[61],"them.":[63],"present":[65],"experiments":[67],"which":[68],"illustrate":[69],"power":[71],"method,":[74],"explore":[75],"behavior,":[78],"compare":[80],"with":[81],"regularized":[82],"flows.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}