{"id":"https://openalex.org/W4308404418","doi":"https://doi.org/10.1515/cmam-2022-0130","title":"Error Estimates for the Numerical Approximation of Unregularized Sparse Parabolic Control Problems","display_name":"Error Estimates for the Numerical Approximation of Unregularized Sparse Parabolic Control Problems","publication_year":2022,"publication_date":"2022-11-07","ids":{"openalex":"https://openalex.org/W4308404418","doi":"https://doi.org/10.1515/cmam-2022-0130"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0130","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0130","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repositorio.unican.es/xmlui/bitstream/10902/30904/2/ErrorEstimatesNumericalApproximation.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067757319","display_name":"Eduardo Casas","orcid":"https://orcid.org/0000-0002-8364-9416"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Eduardo Casas","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n , Universidad de Cantabria , Santander , Spain"],"raw_orcid":"https://orcid.org/0000-0002-8364-9416","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n , Universidad de Cantabria , Santander , Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054687748","display_name":"Mariano Mateos","orcid":"https://orcid.org/0000-0003-3100-412X"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mariano Mateos","raw_affiliation_strings":["Departamento de Matem\u00e1ticas , Universidad de Oviedo , Gij\u00f3n , Spain"],"raw_orcid":"https://orcid.org/0000-0003-3100-412X","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas , Universidad de Oviedo , Gij\u00f3n , Spain","institution_ids":["https://openalex.org/I165339363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054687748"],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22165208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"23","issue":"4","first_page":"877","last_page":"898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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":0.9980000257492065,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.835263192653656},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7328242063522339},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6856334209442139},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.671536386013031},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6685595512390137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5430237054824829},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.45459607243537903},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41924619674682617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25796622037887573},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.2331492006778717},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2174394130706787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11347565054893494}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.835263192653656},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7328242063522339},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6856334209442139},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.671536386013031},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6685595512390137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5430237054824829},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.45459607243537903},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41924619674682617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25796622037887573},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2331492006778717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2174394130706787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11347565054893494},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/cmam-2022-0130","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0130","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unican.es:10902/30904","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/30904","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/30904/2/ErrorEstimatesNumericalApproximation.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Methods in Applied Mathematics, 2023, 23(4), 877-898","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.unican.es:10902/30904","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/30904","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/30904/2/ErrorEstimatesNumericalApproximation.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Methods in Applied Mathematics, 2023, 23(4), 877-898","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2726347730","display_name":null,"funder_award_id":"PID2020-114837GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308404418.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W2005436751","https://openalex.org/W2043551408","https://openalex.org/W2043841940","https://openalex.org/W2046456527","https://openalex.org/W2046922593","https://openalex.org/W2073104520","https://openalex.org/W2079527147","https://openalex.org/W2105253623","https://openalex.org/W2112867735","https://openalex.org/W2139473935","https://openalex.org/W2283798739","https://openalex.org/W2550946907","https://openalex.org/W2727095630","https://openalex.org/W2737426956","https://openalex.org/W2743553439","https://openalex.org/W2791114783","https://openalex.org/W2945491439","https://openalex.org/W2963530777","https://openalex.org/W2963669911","https://openalex.org/W2963679724","https://openalex.org/W3008129455","https://openalex.org/W3102353572","https://openalex.org/W3174503691","https://openalex.org/W3179518325","https://openalex.org/W3204708751","https://openalex.org/W3216105238","https://openalex.org/W4220685398","https://openalex.org/W4253840677","https://openalex.org/W4284971619","https://openalex.org/W6817195152"],"related_works":["https://openalex.org/W2388364587","https://openalex.org/W2337734184","https://openalex.org/W2322955667","https://openalex.org/W2373176546","https://openalex.org/W2127000180","https://openalex.org/W2152224705","https://openalex.org/W2050033254","https://openalex.org/W2561531189","https://openalex.org/W2385735574","https://openalex.org/W2057439054"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"the":[3,17,23],"numerical":[4],"approximation":[5],"of":[6],"a":[7,12,29],"control":[8],"problem":[9],"governed":[10],"by":[11,28],"semilinear":[13],"parabolic":[14],"problem,":[15],"where":[16],"usual":[18],"Tikhonov":[19],"regularization":[20],"term":[21],"in":[22],"cost":[24],"functional":[25],"is":[26],"replaced":[27],"non-differentiable":[30],"sparsity-promoting":[31],"term.":[32]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2022-11-11T00:00:00"}