{"id":"https://openalex.org/W2964267724","doi":"https://doi.org/10.1137/17m1146038","title":"A Trace Finite Element Method for Vector-Laplacians on Surfaces","display_name":"A Trace Finite Element Method for Vector-Laplacians on Surfaces","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2964267724","doi":"https://doi.org/10.1137/17m1146038","mag":"2964267724"},"language":"en","primary_location":{"id":"doi:10.1137/17m1146038","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146038","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/A5005631647","display_name":"Sven Gro\u00df","orcid":"https://orcid.org/0000-0002-6968-4258"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sven Gross","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014274226","display_name":"Thomas Jankuhn","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Jankuhn","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077985757","display_name":"Maxim A. Olshanskii","orcid":"https://orcid.org/0000-0002-9102-6833"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maxim A. Olshanskii","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, Texas 77204-3008"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, Texas 77204-3008","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109253345","display_name":"Arnold Reusken","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Arnold Reusken","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005631647"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":2.9139,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.91215269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"4","first_page":"2406","last_page":"2429"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9987999796867371,"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":0.8196233510971069},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6823062896728516},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6804441213607788},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6541761755943298},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6103627681732178},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5992013812065125},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5767654776573181},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5431848764419556},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4953697919845581},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.47902268171310425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39937326312065125},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19478237628936768},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1824626326560974},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14865398406982422},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.08868500590324402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8196233510971069},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6823062896728516},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6804441213607788},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6541761755943298},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6103627681732178},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5992013812065125},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5767654776573181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5431848764419556},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4953697919845581},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47902268171310425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39937326312065125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19478237628936768},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1824626326560974},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14865398406982422},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.08868500590324402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1146038","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146038","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:publications.rwth-aachen.de:698662","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/698662","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Preprint / igpm, Institut f\u00fcr Geometrie und Praktische Mathematik 469, 23 Seiten (2017).","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1841146072","display_name":null,"funder_award_id":"1717516","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1981344462","https://openalex.org/W1983336409","https://openalex.org/W1984533458","https://openalex.org/W1994672871","https://openalex.org/W2000537156","https://openalex.org/W2003977985","https://openalex.org/W2026623918","https://openalex.org/W2029783443","https://openalex.org/W2039287456","https://openalex.org/W2040896717","https://openalex.org/W2043377185","https://openalex.org/W2050691726","https://openalex.org/W2053364845","https://openalex.org/W2054658778","https://openalex.org/W2073698309","https://openalex.org/W2091458120","https://openalex.org/W2100456139","https://openalex.org/W2147214099","https://openalex.org/W2156149588","https://openalex.org/W2157670588","https://openalex.org/W2335432572","https://openalex.org/W2337287213","https://openalex.org/W2514944159","https://openalex.org/W2548379481","https://openalex.org/W2962885875"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W3146410598","https://openalex.org/W2767153625","https://openalex.org/W1970706285","https://openalex.org/W1982069796","https://openalex.org/W2999046577","https://openalex.org/W2062832849","https://openalex.org/W2053994227"],"abstract_inverted_index":{"We":[0,54,101],"consider":[1],"a":[2,7,12,41,67,98,163],"vector-Laplace":[3],"problem":[4,149],"posed":[5],"on":[6,24,66,126],"two-dimensional":[8],"surface":[9,21,50,74,95],"embedded":[10],"in":[11,61],"three-dimensional":[13],"domain,":[14],"which":[15,62,118],"results":[16],"from":[17],"the":[18,36,46,56,84,87,94,105,144],"modeling":[19],"of":[20,32,40,48,104,113,143,162],"fluids":[22],"based":[23,125],"exterior":[25],"Cartesian":[26],"differential":[27,52],"operators.":[28],"The":[29],"main":[30],"topic":[31],"this":[33,49,114,132],"paper":[34],"is":[35,73,91,116,124,159],"development":[37],"and":[38,123],"analysis":[39],"finite":[42,58,63,128],"element":[43,59,64,129],"method":[44,133],"for":[45,78],"discretization":[47,137],"partial":[51],"equation.":[53],"apply":[55],"trace":[57,127],"technique,":[60],"spaces":[65],"background":[68],"shape-regular":[69],"tetrahedral":[70],"mesh":[71],"that":[72,86],"independent":[75],"are":[76,150,166],"used":[77],"discretization.":[79],"In":[80,152],"order":[81],"to":[82,93],"satisfy":[83],"constraint":[85],"solution":[88],"vector":[89],"field":[90],"tangential":[92],"we":[96,134],"introduce":[97],"Lagrange":[99],"multiplier.":[100],"show":[102],"well-posedness":[103],"resulting":[106,145],"saddle":[107,147],"point":[108,148],"formulation.":[109],"A":[110],"discrete":[111,146],"variant":[112],"formulation":[115],"introduced":[117],"contains":[119],"suitable":[120],"stabilization":[121],"terms":[122],"spaces.":[130],"For":[131],"derive":[135],"optimal":[136,155],"error":[138],"bounds.":[139],"Furthermore":[140],"algebraic":[141],"properties":[142],"studied.":[151],"particular":[153],"an":[154],"Schur":[156],"complement":[157],"preconditioner":[158],"proposed.":[160],"Results":[161],"numerical":[164],"experiment":[165],"included.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}