{"id":"https://openalex.org/W2798966834","doi":"https://doi.org/10.1137/18m1169886","title":"A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics","display_name":"A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2798966834","doi":"https://doi.org/10.1137/18m1169886","mag":"2798966834"},"language":"en","primary_location":{"id":"doi:10.1137/18m1169886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169886","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062969935","display_name":"L. Beir\u00e3o da Veiga","orcid":"https://orcid.org/0000-0001-5895-469X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Beira\u0342o da Veiga","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073696154","display_name":"Franco Brezzi","orcid":"https://orcid.org/0000-0003-4715-5475"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Brezzi","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4715-5475","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032113772","display_name":"Franco Dassi","orcid":"https://orcid.org/0000-0001-5590-3651"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Dassi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056811351","display_name":"L. D. Marini","orcid":"https://orcid.org/0000-0002-9224-1367"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. D. Marini","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9224-1367","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056593294","display_name":"A. Russo","orcid":"https://orcid.org/0000-0002-6878-402X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Russo","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":3.9136,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.94644857,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"5","first_page":"2940","last_page":"2962"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.6157485246658325},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.534314751625061},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.48298752307891846},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.4638272523880005},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4487419128417969},{"id":"https://openalex.org/keywords/serendipity","display_name":"Serendipity","score":0.42295658588409424},{"id":"https://openalex.org/keywords/magnetostatics","display_name":"Magnetostatics","score":0.41691604256629944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3541669249534607},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33900120854377747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2294251024723053},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07492810487747192}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6157485246658325},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.534314751625061},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.48298752307891846},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.4638272523880005},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4487419128417969},{"id":"https://openalex.org/C2779119418","wikidata":"https://www.wikidata.org/wiki/Q166039","display_name":"Serendipity","level":2,"score":0.42295658588409424},{"id":"https://openalex.org/C95390329","wikidata":"https://www.wikidata.org/wiki/Q665093","display_name":"Magnetostatics","level":3,"score":0.41691604256629944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3541669249534607},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33900120854377747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2294251024723053},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07492810487747192},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1169886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1169886","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:boa.unimib.it:10281/212791","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/212791","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1009522003","https://openalex.org/W1965816824","https://openalex.org/W1986187395","https://openalex.org/W1986364072","https://openalex.org/W1994687200","https://openalex.org/W1996774337","https://openalex.org/W1998894128","https://openalex.org/W2006000775","https://openalex.org/W2045686441","https://openalex.org/W2047049848","https://openalex.org/W2051752778","https://openalex.org/W2057105966","https://openalex.org/W2061524394","https://openalex.org/W2062807652","https://openalex.org/W2072855901","https://openalex.org/W2089142741","https://openalex.org/W2126086928","https://openalex.org/W2130350269","https://openalex.org/W2130763970","https://openalex.org/W2157252460","https://openalex.org/W2161234659","https://openalex.org/W2161530217","https://openalex.org/W2168914934","https://openalex.org/W2169464027","https://openalex.org/W2325830745","https://openalex.org/W2328294984","https://openalex.org/W2328450917","https://openalex.org/W2339371798","https://openalex.org/W2524960348","https://openalex.org/W2571957007","https://openalex.org/W2604221186","https://openalex.org/W2621407111","https://openalex.org/W2684097608","https://openalex.org/W2746576719","https://openalex.org/W2751927746","https://openalex.org/W2764120414","https://openalex.org/W2963034144","https://openalex.org/W2963131956","https://openalex.org/W2963651557","https://openalex.org/W2963893869","https://openalex.org/W2964170036","https://openalex.org/W2964307594"],"related_works":["https://openalex.org/W4205615116","https://openalex.org/W2154428221","https://openalex.org/W2531086667","https://openalex.org/W35325473","https://openalex.org/W1876349746","https://openalex.org/W3125216959","https://openalex.org/W2045676999","https://openalex.org/W2765630348","https://openalex.org/W2009287061","https://openalex.org/W2094293761"],"abstract_inverted_index":{"We":[0],"consider,":[1],"as":[2],"a":[3,46],"simple":[4],"model":[5],"problem,":[6],"the":[7,15,21,36,43,72],"application":[8],"of":[9,23,45,54,75],"virtual":[10],"element":[11],"methods":[12],"(VEMs)":[13],"to":[14],"linear":[16],"magnetostatic":[17],"three-dimensional":[18],"problem":[19],"in":[20,85,98],"formulation":[22],"Kikuchi.":[24],"In":[25],"doing":[26],"so,":[27],"we":[28],"also":[29],"introduce":[30],"new":[31,65],"serendipity":[32,37],"VEM":[33],"spaces,":[34],"where":[35],"reduction":[38],"is":[39],"made":[40],"only":[41],"on":[42],"faces":[44],"general":[47,100],"polyhedral":[48],"decomposition":[49],"(assuming":[50],"that":[51],"internal":[52],"degrees":[53],"freedom":[55],"could":[56,90],"be":[57,92],"more":[58,69,99],"easily":[59],"eliminated":[60],"by":[61],"static":[62],"condensation).":[63],"These":[64],"spaces":[66,84],"are":[67],"meant,":[68],"generally,":[70],"for":[71,94],"combined":[73],"approximation":[74],"$H^1$-conforming":[76],"(0-forms),":[77],"$H(curl)$-conforming":[78],"(1-forms),":[79],"and":[80,88,97],"$H(div)$-conforming":[81],"(2-forms)":[82],"functional":[83],"three":[86],"dimensions,":[87],"they":[89],"surely":[91],"useful":[93],"other":[95],"problems":[96],"contexts.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
