{"id":"https://openalex.org/W7128537631","doi":"https://doi.org/10.48550/arxiv.2602.08967","title":"Convergence Analysis for the Recovery of the Friction Threshold in a Scalar Tresca Model","display_name":"Convergence Analysis for the Recovery of the Friction Threshold in a Scalar Tresca Model","publication_year":2026,"publication_date":"2026-02-09","ids":{"openalex":"https://openalex.org/W7128537631","doi":"https://doi.org/10.48550/arxiv.2602.08967"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.08967","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.08967","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.08967","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011409848","display_name":"Erik Burman","orcid":"https://orcid.org/0000-0003-4287-7241"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Burman, Erik","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081620253","display_name":"Marvin Kn\u00f6ller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kn\u00f6ller, Marvin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014787639","display_name":"Lauri Oksanen","orcid":"https://orcid.org/0000-0003-1006-1520"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oksanen, Lauri","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005892048","display_name":"Andreas Rupp","orcid":"https://orcid.org/0000-0001-5527-7187"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rupp, Andreas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011409848"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.6550999879837036,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.6550999879837036,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.21570000052452087,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.03819999843835831,"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/partial-differential-equation","display_name":"Partial differential equation","score":0.6549000144004822},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5573999881744385},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5472999811172485},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49380001425743103},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.40459999442100525},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4041000008583069},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3955000042915344},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.39329999685287476},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.38999998569488525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7958999872207642},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6549000144004822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6201000213623047},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5573999881744385},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5472999811172485},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39649999141693115},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.3847000002861023},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.29159998893737793},{"id":"https://openalex.org/C65826597","wikidata":"https://www.wikidata.org/wiki/Q17099589","display_name":"Poincar\u00e9\u2013Steklov operator","level":5,"score":0.2838999927043915},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.26980000734329224}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.08967","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.08967","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.08967","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.08967","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,131,166],"consider":[1],"a":[2,10,17,24,33,66,142],"scalar":[3],"valued":[4],"elliptic":[5],"partial":[6,81,92],"differential":[7,82,93],"equation":[8,83,94],"on":[9,23,95,126],"sufficiently":[11],"smooth":[12],"domain":[13],"$\u03a9$,":[14],"subject":[15],"to":[16,43,51,90,121,141,160],"regularized":[18],"Tresca":[19],"friction-type":[20],"boundary":[21,39],"condition":[22],"subset":[25,99],"$\u0393$":[26],"of":[27,79,113],"$\\partial":[28],"\u03a9$.":[29],"The":[30],"friction":[31,62,115,164],"threshold,":[32],"positive":[34],"function":[35,143],"appearing":[36],"in":[37,54,65,138,150,153],"this":[38],"condition,":[40],"is":[41,102,119,124],"assumed":[42],"be":[44,52],"unknown":[45],"and":[46,86,123],"serves":[47],"as":[48],"the":[49,61,75,80,88,91,111,114,134,154,161],"coefficient":[50],"recovered":[53],"our":[55,168,175],"inverse":[56],"problem.":[57],"Assuming":[58],"that":[59,133,147,173],"(i)":[60],"threshold":[63],"lies":[64],"finite":[67,129,155],"dimensional":[68],"space":[69],"with":[70],"known":[71],"basis":[72],"functions,":[73],"(ii)":[74],"right":[76],"hand":[77],"sides":[78],"are":[84],"known,":[85],"(iii)":[87],"solution":[89],"some":[96],"small":[97],"open":[98],"$\u03c9\\subset":[100],"\u03a9$":[101],"available,":[103],"we":[104],"develop":[105],"an":[106],"iterative":[107],"computational":[108],"method":[109],"for":[110],"recovery":[112],"threshold.":[116,165],"This":[117],"algorithm":[118,136],"simple":[120],"implement":[122],"based":[125],"piecewise":[127],"linear":[128],"elements.":[130],"show":[132],"proposed":[135],"converges":[137,149],"second":[139,151],"order":[140,152],"$a_h$":[144,148],"and,":[145],"moreover,":[146],"element's":[156],"mesh":[157],"size":[158],"$h$":[159],"true":[162],"(unknown)":[163],"highlight":[167],"theoretical":[169],"results":[170],"by":[171],"simulations":[172],"confirm":[174],"rates":[176],"numerically.":[177]},"counts_by_year":[],"updated_date":"2026-02-11T14:45:31.134243","created_date":"2026-02-11T00:00:00"}