{"id":"https://openalex.org/W3154589321","doi":"https://doi.org/10.1137/20m1312927","title":"Random finite-difference discretizations of the ambrosio\u2013tortorelli functional with optimal mesh-size","display_name":"Random finite-difference discretizations of the ambrosio\u2013tortorelli functional with optimal mesh-size","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3154589321","doi":"https://doi.org/10.1137/20m1312927","mag":"3154589321"},"language":"en","primary_location":{"id":"pmh:oai:iris.uniroma1.it:11573/1559086","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1559086","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11573/1559086","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112204705","display_name":"Annika Bach","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bach, Annika","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011286546","display_name":"Marco Cicalese","orcid":"https://orcid.org/0000-0003-3650-4078"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cicalese, Marco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044103864","display_name":"Matthias Ruf","orcid":"https://orcid.org/0000-0003-4720-410X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruf, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0128,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79236675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"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":0.9984999895095825,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983999729156494,"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":0.9923999905586243,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8606479167938232},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5310081839561462},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4731779396533966},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4695121943950653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4121784567832947}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8606479167938232},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5310081839561462},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4731779396533966},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4695121943950653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4121784567832947}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:iris.uniroma1.it:11573/1559086","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1559086","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:113751","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/113751","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:iris.uniroma1.it:11573/1559086","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1559086","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3365634815","display_name":null,"funder_award_id":"QUANTHOM 335410","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1603576422","https://openalex.org/W1985349496","https://openalex.org/W1990620164","https://openalex.org/W1995764344","https://openalex.org/W2010840867","https://openalex.org/W2012949880","https://openalex.org/W2017025711","https://openalex.org/W2020999234","https://openalex.org/W2047647776","https://openalex.org/W2083623174","https://openalex.org/W2086002908","https://openalex.org/W2087655772","https://openalex.org/W2105403267","https://openalex.org/W2114487471","https://openalex.org/W2121713293","https://openalex.org/W2155280009","https://openalex.org/W2165734775","https://openalex.org/W2963694945","https://openalex.org/W3081899042","https://openalex.org/W3100021303","https://openalex.org/W3101039200","https://openalex.org/W3105916497","https://openalex.org/W4239097771"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W2766044013","https://openalex.org/W2007426143","https://openalex.org/W56705272","https://openalex.org/W2384221708","https://openalex.org/W2171402820","https://openalex.org/W2044635454"],"abstract_inverted_index":{"We":[0],"propose":[1],"and":[2,59],"analyze":[3],"a":[4,73,82],"finite-difference":[5],"discretization":[6,17,78,112],"of":[7,27,49,91,119,132],"the":[8,16,30,35,45,50,77,92,104,109,116,129],"Ambrosio\u2013Tortorelli":[9,51],"functional.":[10,52,94],"It":[11],"is":[12,18,101,108,118],"known":[13],"that":[14,98,106],"if":[15,39],"made":[19],"with":[20,54,79],"respect":[21,55,80],"to":[22,34,56,81,87],"an":[23,88],"underlying":[24],"periodic":[25,83],"lattice":[26,84],"spacing":[28],"\u03b4,":[29],"discretized":[31],"functionals":[32],"\u0393-converge":[33],"Mumford\u2013Shah":[36,93,120],"functional":[37],"only":[38],"\u03b4":[40,70],"\u227c":[41],"\u03b5,":[42,72],"\u03b5":[43],"being":[44],"elliptic":[46],"approximation":[47],"parameter":[48],"Discretizing":[53],"stationary,":[57],"ergodic,":[58],"isotropic":[60,130],"random":[61,134],"lattices":[62],"we":[63,96,123],"prove":[64],"this":[65,99],"\u0393-convergence":[66],"result":[67],"also":[68],"for":[69,114],"\u223c":[71],"regime":[74],"at":[75],"which":[76,115],"converges":[85],"instead":[86],"anisotropic":[89],"version":[90],"Moreover,":[95],"show":[97],"scaling":[100],"optimal":[102],"in":[103],"sense":[105],"it":[107],"largest":[110],"possible":[111],"scale":[113],"\u0393-limit":[117],"type.":[121],"Finally,":[122],"present":[124],"some":[125],"numerical":[126],"results":[127],"highlighting":[128],"behavior":[131],"our":[133],"discrete":[135],"functionals.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-10T07:45:09.275182","created_date":"2021-04-26T00:00:00"}