{"id":"https://openalex.org/W2779831244","doi":"https://doi.org/10.1137/17m1163335","title":"Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem","display_name":"Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2779831244","doi":"https://doi.org/10.1137/17m1163335","mag":"2779831244"},"language":"en","primary_location":{"id":"doi:10.1137/17m1163335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1163335","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.10172","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":"Erik Burman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077614976","display_name":"Mats G. Larson","orcid":"https://orcid.org/0000-0001-5589-4521"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mats G. Larson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044437642","display_name":"Lauri Oksanen","orcid":"https://orcid.org/0000-0002-3228-7507"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lauri Oksanen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011409848"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3648,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50829128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"56","issue":"6","first_page":"3480","last_page":"3509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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/mathematics","display_name":"Mathematics","score":0.7809181213378906},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.6651856899261475},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5928031206130981},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.564041256904602},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5606764554977417},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5426322817802429},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.41313791275024414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37876468896865845},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.193078875541687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0902533233165741}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7809181213378906},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.6651856899261475},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5928031206130981},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.564041256904602},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5606764554977417},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5426322817802429},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.41313791275024414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37876468896865845},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.193078875541687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0902533233165741},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1163335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1163335","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"},{"id":"pmh:oai:arXiv.org:1712.10172","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.10172","pdf_url":"https://arxiv.org/pdf/1712.10172","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2779831244","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1712.10172.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10060887","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10060887/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM Journal on Numerical Analysis , 56  (6)   pp. 3480-3509.   (2018)      ","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1712.10172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.10172","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":"pmh:oai:arXiv.org:1712.10172","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.10172","pdf_url":"https://arxiv.org/pdf/1712.10172","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G1113386463","display_name":null,"funder_award_id":"2017-03911","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G1982737232","display_name":null,"funder_award_id":"EP/P01576X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3413367412","display_name":null,"funder_award_id":"AM13-0029","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3473563908","display_name":null,"funder_award_id":"2013-04708","funder_id":"https://openalex.org/F4320321033","funder_display_name":"Svenska Forskningsr\u00e5det Formas"},{"id":"https://openalex.org/G3998745228","display_name":null,"funder_award_id":"AM13-0029","funder_id":"https://openalex.org/F4320320940","funder_display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning"},{"id":"https://openalex.org/G4293385531","display_name":"Optimising patient specific treatment plans for ultrasound ablative therapies in the abdomen (OptimUS)","funder_award_id":"EP/P012434/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5108271548","display_name":null,"funder_award_id":"EP/N026942/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5150450285","display_name":"Inverse problems for hyperbolic partial differential equations","funder_award_id":"EP/P01593X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5351140740","display_name":"The inverse source problem arising in Photoacoustic Tomography","funder_award_id":"EP/L026473/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5648043610","display_name":null,"funder_award_id":"AM13-0029","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G5821180939","display_name":null,"funder_award_id":"2017-03911","funder_id":"https://openalex.org/F4320321033","funder_display_name":"Svenska Forskningsr\u00e5det Formas"},{"id":"https://openalex.org/G6552244860","display_name":null,"funder_award_id":"EP/P01593X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7884004242","display_name":null,"funder_award_id":"2017-03911","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G797993351","display_name":"Geometrically unfitted finite element methods for inverse identification of geometries and shape optimization","funder_award_id":"EP/P01576X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8719353587","display_name":null,"funder_award_id":"EP/P0","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8733680981","display_name":null,"funder_award_id":"EP/P012434/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8863664214","display_name":null,"funder_award_id":"EP/L026473/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320940","display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning","ror":"https://ror.org/044wr7g58"},{"id":"https://openalex.org/F4320321033","display_name":"Svenska Forskningsr\u00e5det Formas","ror":"https://ror.org/03pjs1y45"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2779831244.pdf","grobid_xml":"https://content.openalex.org/works/W2779831244.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1934446659","https://openalex.org/W1965034652","https://openalex.org/W1974331835","https://openalex.org/W1979771104","https://openalex.org/W1984584765","https://openalex.org/W1991686312","https://openalex.org/W2004259617","https://openalex.org/W2009482684","https://openalex.org/W2011695259","https://openalex.org/W2031838089","https://openalex.org/W2042330229","https://openalex.org/W2042598996","https://openalex.org/W2048719210","https://openalex.org/W2050833124","https://openalex.org/W2059687507","https://openalex.org/W2073572636","https://openalex.org/W2082187902","https://openalex.org/W2085315092","https://openalex.org/W2521794430","https://openalex.org/W2530858181","https://openalex.org/W2591763202","https://openalex.org/W2963671148","https://openalex.org/W2963917324","https://openalex.org/W3003932625","https://openalex.org/W4248122039"],"related_works":["https://openalex.org/W1732796942","https://openalex.org/W2344009218","https://openalex.org/W2227962568","https://openalex.org/W2768306041","https://openalex.org/W2402890574","https://openalex.org/W2165630134","https://openalex.org/W2061969432","https://openalex.org/W2076578213","https://openalex.org/W3008227064","https://openalex.org/W2002935642","https://openalex.org/W1539940514","https://openalex.org/W3183558511","https://openalex.org/W2984161868","https://openalex.org/W2907980666","https://openalex.org/W2938794897","https://openalex.org/W2940921728","https://openalex.org/W2790726926","https://openalex.org/W2902148665","https://openalex.org/W2739359106","https://openalex.org/W3003890753"],"abstract_inverted_index":{"We":[0,28],"consider":[1],"primal-dual":[2],"mixed":[3,95],"finite":[4,96],"element":[5,97],"methods":[6],"for":[7,55,147],"the":[8,11,41,73,82,92,129,133,141,153,156],"solution":[9,154],"of":[10,44,61,72,81,91,121,155],"elliptic":[12],"Cauchy":[13],"problem,":[14],"or":[15],"other":[16],"related":[17],"data":[18,64],"assimilation":[19],"problems.":[20],"The":[21,59,114,159],"method":[22,98,143],"has":[23],"a":[24,30,78,89],"local":[25],"conservation":[26],"property.":[27],"derive":[29],"priori":[31],"error":[32],"estimates":[33,38],"using":[34],"known":[35],"conditional":[36],"stability":[37],"and":[39,48,103],"determine":[40,152],"minimal":[42],"amount":[43],"weakly":[45],"consistent":[46],"stabilization":[47,80],"Tikhonov":[49],"regularization":[50,122],"that":[51,118,140],"yields":[52],"optimal":[53],"convergence":[54],"smooth":[56],"exact":[57],"solutions.":[58],"effect":[60],"perturbations":[62],"in":[63,105],"is":[65,117,161],"also":[66],"accounted":[67],"for.":[68],"A":[69],"reduced":[70,142],"version":[71],"method,":[74],"obtained":[75],"by":[76,100,163],"choosing":[77],"special":[79],"dual":[83],"variable,":[84],"can":[85,144],"be":[86,145],"viewed":[87],"as":[88],"variant":[90],"least":[93],"squares":[94],"introduced":[99],"Dard\u00e9,":[101],"Hannukainen,":[102],"Hyv\u00f6nen":[104],"[SIAM":[106],"J.":[107],"Numer.":[108],"Anal.,":[109],"51":[110],"(2013),":[111],"pp.":[112],"2123--2148].":[113],"main":[115],"difference":[116],"our":[119],"choice":[120],"does":[123],"not":[124],"depend":[125],"on":[126],"auxiliary":[127],"parameters,":[128],"mesh":[130],"size":[131],"being":[132],"only":[134],"asymptotic":[135],"parameter.":[136],"Finally,":[137],"we":[138],"show":[139],"used":[146],"defect":[148],"correction":[149],"iteration":[150],"to":[151],"full":[157],"method.":[158],"theory":[160],"illustrated":[162],"some":[164],"numerical":[165],"examples.":[166]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}