{"id":"https://openalex.org/W2088612743","doi":"https://doi.org/10.1137/140954477","title":"Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem","display_name":"Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2088612743","doi":"https://doi.org/10.1137/140954477","mag":"2088612743"},"language":"en","primary_location":{"id":"doi:10.1137/140954477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140954477","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11311/990589","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077685861","display_name":"Takahito Kashiwabara","orcid":"https://orcid.org/0000-0002-7089-8202"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["CH","JP"],"is_corresponding":true,"raw_author_name":"Takahito Kashiwabara","raw_affiliation_strings":["Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan","CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland"],"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085470188","display_name":"Claudia Maria Colciago","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Claudia Maria Colciago","raw_affiliation_strings":["CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland"],"affiliations":[{"raw_affiliation_string":"CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034191028","display_name":"Luca Dede\u2019","orcid":"https://orcid.org/0000-0002-6558-8277"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Ded\u00e8","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013754088","display_name":"Alfio Quarteroni","orcid":"https://orcid.org/0000-0002-5947-6885"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","IT"],"is_corresponding":false,"raw_author_name":"Alfio Quarteroni","raw_affiliation_strings":["CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland","MOX, Department of Mathematics, Politecnico di Milano, Piazza L. da Vinci 32, Milano, 20133, Italy"],"affiliations":[{"raw_affiliation_string":"CMCS-MATHICSE-SB, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Av. Picard, Station 8, Lausanne, CH-1015, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"MOX, Department of Mathematics, Politecnico di Milano, Piazza L. da Vinci 32, Milano, 20133, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5077685861"],"corresponding_institution_ids":["https://openalex.org/I5124864","https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":3.2744,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.92421366,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"1","first_page":"105","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.870622992515564},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6236327290534973},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.6050440073013306},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5750043392181396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5232471823692322},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5063172578811646},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4760827124118805},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.45784348249435425},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.4510495066642761},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4416271448135376},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3402160406112671},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.2871214747428894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.870622992515564},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6236327290534973},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.6050440073013306},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5750043392181396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5232471823692322},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5063172578811646},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4760827124118805},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.45784348249435425},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.4510495066642761},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4416271448135376},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3402160406112671},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.2871214747428894},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140954477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140954477","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:re.public.polimi.it:11311/990589","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/990589","pdf_url":"http://hdl.handle.net/11311/990589","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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:infoscience.epfl.ch:204566","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/204566","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:re.public.polimi.it:11311/990589","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/990589","pdf_url":"http://hdl.handle.net/11311/990589","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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":[],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2088612743.pdf","grobid_xml":"https://content.openalex.org/works/W2088612743.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W44035921","https://openalex.org/W155722398","https://openalex.org/W311630916","https://openalex.org/W642107583","https://openalex.org/W815434344","https://openalex.org/W967279735","https://openalex.org/W1480366635","https://openalex.org/W1545761024","https://openalex.org/W1558045032","https://openalex.org/W1577348790","https://openalex.org/W1597209545","https://openalex.org/W1866311589","https://openalex.org/W1974920483","https://openalex.org/W1983332762","https://openalex.org/W1984480729","https://openalex.org/W1988326784","https://openalex.org/W2000425991","https://openalex.org/W2000450704","https://openalex.org/W2000582360","https://openalex.org/W2007466958","https://openalex.org/W2007510482","https://openalex.org/W2020920275","https://openalex.org/W2032740120","https://openalex.org/W2041523977","https://openalex.org/W2056771931","https://openalex.org/W2058621793","https://openalex.org/W2059512870","https://openalex.org/W2062761986","https://openalex.org/W2067824277","https://openalex.org/W2071036364","https://openalex.org/W2073291771","https://openalex.org/W2073370369","https://openalex.org/W2074623661","https://openalex.org/W2081746320","https://openalex.org/W2082265985","https://openalex.org/W2096192204","https://openalex.org/W2104730330","https://openalex.org/W2130118020","https://openalex.org/W2139993731","https://openalex.org/W2148835848","https://openalex.org/W2323813563","https://openalex.org/W2608849428","https://openalex.org/W4248161126"],"related_works":["https://openalex.org/W4254213601","https://openalex.org/W2196719869","https://openalex.org/W2488373638","https://openalex.org/W2100299603","https://openalex.org/W1589056410","https://openalex.org/W3136311820","https://openalex.org/W2092505998","https://openalex.org/W2148234322","https://openalex.org/W2897990565","https://openalex.org/W2905205127"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,50],"propose":[4],"the":[5,26,53,56,68,72,75,88,93,97,103,106,110],"mathematical":[6],"and":[7],"finite":[8,89],"element":[9,90],"analysis":[10],"of":[11,36,55,74,87,95,100,102],"a":[12,19,31,47,63],"second-order":[13],"partial":[14],"differential":[15],"equation":[16],"endowed":[17],"with":[18,38,92],"generalized":[20,57,82],"Robin":[21,58,77,83],"boundary":[22,59,69],"condition":[23],"which":[24],"involves":[25],"Laplace--Beltrami":[27],"operator":[28],"by":[29,85],"introducing":[30],"function":[32],"space":[33,111],"$H^1(\\Omega;":[34,112],"\\Gamma)$":[35],"$H^1(\\Omega)$-functions":[37],"$H^1(\\Gamma)$-traces,":[39],"where":[40],"$\\Gamma":[41],"\\subseteq":[42],"\\partial":[43],"\\Omega$.":[44],"Based":[45],"on":[46,67],"variational":[48],"method,":[49],"prove":[51],"that":[52],"solution":[54],"value":[60],"problem":[61],"possesses":[62],"better":[64],"regularity":[65],"property":[66],"than":[70],"in":[71,105],"case":[73],"standard":[76],"problem.":[78],"We":[79],"numerically":[80],"solve":[81],"problems":[84],"means":[86],"method":[91],"aim":[94],"validating":[96],"theoretical":[98],"rates":[99],"convergence":[101],"error":[104],"norms":[107],"associated":[108],"to":[109],"\\Gamma)$.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
