{"id":"https://openalex.org/W2170299747","doi":"https://doi.org/10.1137/070698798","title":"Polynomial Extension Operators. Part II","display_name":"Polynomial Extension Operators. Part II","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2170299747","doi":"https://doi.org/10.1137/070698798","mag":"2170299747"},"language":"en","primary_location":{"id":"doi:10.1137/070698798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698798","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/A5082045365","display_name":"Leszek Demkowicz","orcid":"https://orcid.org/0000-0001-7839-8037"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leszek Demkowicz","raw_affiliation_strings":["leszek@ices.utexas.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"leszek@ices.utexas.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022236310","display_name":"Jay Gopalakrishnan","orcid":"https://orcid.org/0000-0001-7508-3232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jayadeep Gopalakrishnan","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021823634","display_name":"Joachim Sch\u00f6berl","orcid":"https://orcid.org/0000-0002-1250-5087"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joachim Sch\u00f6berl","raw_affiliation_strings":["joachim.schoeberl@rwth-aachen.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"joachim.schoeberl@rwth-aachen.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7768,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.91120876,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"47","issue":"5","first_page":"3293","last_page":"3324"},"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":1.0,"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":1.0,"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":0.9993000030517578,"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":0.8412034511566162},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6494713425636292},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6292905807495117},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6053282022476196},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5899579524993896},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.508021354675293},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.4674466848373413},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4539269804954529},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39312994480133057},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36913806200027466},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3185371160507202},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1839035451412201},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06525963544845581}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8412034511566162},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6494713425636292},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6292905807495117},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6053282022476196},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5899579524993896},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.508021354675293},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.4674466848373413},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4539269804954529},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39312994480133057},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36913806200027466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3185371160507202},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1839035451412201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06525963544845581},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":5,"locations":[{"id":"doi:10.1137/070698798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698798","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:pdxscholar.library.pdx.edu:mth_fac-1056","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/57","pdf_url":null,"source":{"id":"https://openalex.org/S4377196300","display_name":"PDXScholar  (Portland State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126345244","host_organization_name":"Portland State University","host_organization_lineage":["https://openalex.org/I126345244"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Faculty Publications and Presentations","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.1047","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.1047","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ufl.edu/~jayg/pub/extHcurl.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.184.4634","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.4634","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ufl.edu/%7Ejayg/pub/extHcurl.pdf","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:188682","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/188682","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","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":"SIAM journal on numerical analysis 47(5), 3293-3324 (2009). doi:10.1137/070698798","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W59705922","https://openalex.org/W107777212","https://openalex.org/W560409768","https://openalex.org/W1485193345","https://openalex.org/W1488877410","https://openalex.org/W1533613088","https://openalex.org/W1537887709","https://openalex.org/W1582734821","https://openalex.org/W1586623601","https://openalex.org/W1589558795","https://openalex.org/W1597209545","https://openalex.org/W1602383637","https://openalex.org/W1674659126","https://openalex.org/W1969732357","https://openalex.org/W1969923739","https://openalex.org/W1982316836","https://openalex.org/W1985861577","https://openalex.org/W1989248758","https://openalex.org/W1994484297","https://openalex.org/W1995613081","https://openalex.org/W1998829387","https://openalex.org/W2026892575","https://openalex.org/W2029243375","https://openalex.org/W2031933307","https://openalex.org/W2042556046","https://openalex.org/W2051682834","https://openalex.org/W2054896264","https://openalex.org/W2058266517","https://openalex.org/W2059975982","https://openalex.org/W2062618977","https://openalex.org/W2068768492","https://openalex.org/W2074076160","https://openalex.org/W2075478495","https://openalex.org/W2077670970","https://openalex.org/W2085059933","https://openalex.org/W2088259936","https://openalex.org/W2116663540","https://openalex.org/W2325830745","https://openalex.org/W2525823748","https://openalex.org/W2606980654","https://openalex.org/W4240668518","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2382844561","https://openalex.org/W2083529992","https://openalex.org/W816511862","https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W2238883956","https://openalex.org/W3119989344","https://openalex.org/W2799711503","https://openalex.org/W2948362504","https://openalex.org/W3091849091"],"abstract_inverted_index":{"Consider":[0],"the":[1,9,29,38],"tangential":[2],"trace":[3,23,39],"of":[4,11,41,58,67],"a":[5,12,22,26,46,64],"vector":[6],"polynomial":[7,27],"on":[8,28],"surface":[10],"tetrahedron.":[13,30],"We":[14],"construct":[15],"an":[16,50],"extension":[17,51],"operator":[18,32,52],"that":[19],"extends":[20],"such":[21],"function":[24],"into":[25],"This":[31],"can":[33],"be":[34],"continuously":[35],"extended":[36],"to":[37],"space":[40],"$H(\\mathbf{curl}\\,)$.":[42],"Furthermore,":[43],"it":[44],"satisfies":[45],"commutativity":[47],"property":[48],"with":[49],"we":[53],"constructed":[54],"in":[55],"Part":[56],"I":[57],"this":[59],"series.":[60],"Such":[61],"extensions":[62],"are":[63],"fundamental":[65],"ingredient":[66],"high":[68],"order":[69],"finite":[70],"element":[71],"analysis.":[72]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
