{"id":"https://openalex.org/W2089907194","doi":"https://doi.org/10.1090/s0025-5718-2011-02536-6","title":"Polynomial extension operators. Part III","display_name":"Polynomial extension operators. Part III","publication_year":2011,"publication_date":"2011-09-20","ids":{"openalex":"https://openalex.org/W2089907194","doi":"https://doi.org/10.1090/s0025-5718-2011-02536-6","mag":"2089907194"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02536-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02536-6","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02536-6/S0025-5718-2011-02536-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02536-6/S0025-5718-2011-02536-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073036341","display_name":"L. Demkowicz","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Demkowicz","raw_affiliation_strings":["Institute of Computational Engineering and Sciences, 1 University Station, C0200, The University of Texas at Austin, Texas 78712"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computational Engineering and Sciences, 1 University Station, C0200, The University of Texas at Austin, Texas 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022236310","display_name":"Jay Gopalakrishnan","orcid":"https://orcid.org/0000-0001-7508-3232"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Gopalakrishnan","raw_affiliation_strings":["University of Florida, Department of Mathematics, Gainesville, Florida 32611\u00e2\u0080\u00938105","University of Florida, Department of Mathematics, Gainesville, Florida 32611\u20138105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Department of Mathematics, Gainesville, Florida 32611\u00e2\u0080\u00938105","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"University of Florida, Department of Mathematics, Gainesville, Florida 32611\u20138105","institution_ids":["https://openalex.org/I33213144"]}]},{"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":"J. Sch\u00f6berl","raw_affiliation_strings":["Technische Universit\u00e4t Wein, Wiedner Hauptstrasse 8-10, Wein 1040, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Wein, Wiedner Hauptstrasse 8-10, Wein 1040, Austria","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7081,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.84193261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"81","issue":"279","first_page":"1289","last_page":"1326"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.8243096470832825},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6919333934783936},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6884342432022095},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6449093818664551},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6028082370758057},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.547685444355011},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.545259952545166},{"id":"https://openalex.org/keywords/trace-operator","display_name":"Trace operator","score":0.493958055973053},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.4678381681442261},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.46024221181869507},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4381714165210724},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42750993371009827},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42541176080703735},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3858181834220886},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3333887457847595},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13829931616783142},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.0785108208656311}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8243096470832825},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6919333934783936},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6884342432022095},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6449093818664551},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6028082370758057},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.547685444355011},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.545259952545166},{"id":"https://openalex.org/C182480750","wikidata":"https://www.wikidata.org/wiki/Q13581708","display_name":"Trace operator","level":5,"score":0.493958055973053},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.4678381681442261},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.46024221181869507},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4381714165210724},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42750993371009827},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42541176080703735},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3858181834220886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3333887457847595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13829931616783142},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.0785108208656311},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C94242865","wikidata":"https://www.wikidata.org/wiki/Q5365788","display_name":"Elliptic boundary value problem","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02536-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02536-6","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02536-6/S0025-5718-2011-02536-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:pdxscholar.library.pdx.edu:mth_fac-1043","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/44","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:10.1.1.726.511","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.726.511","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.asc.tuwien.ac.at/%7Eschoeberl/wiki/publications/paperHdiv.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02536-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02536-6","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02536-6/S0025-5718-2011-02536-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2366464864","display_name":"Novel mixed and DG methods","funder_award_id":"1014817","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/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2089907194.pdf","grobid_xml":"https://content.openalex.org/works/W2089907194.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W59705922","https://openalex.org/W1485193345","https://openalex.org/W1488877410","https://openalex.org/W1582734821","https://openalex.org/W1674659126","https://openalex.org/W1969923739","https://openalex.org/W1982316836","https://openalex.org/W1985861577","https://openalex.org/W1994484297","https://openalex.org/W2026892575","https://openalex.org/W2031933307","https://openalex.org/W2051682834","https://openalex.org/W2054896264","https://openalex.org/W2068768492","https://openalex.org/W2085059933","https://openalex.org/W2088259936","https://openalex.org/W2116663540","https://openalex.org/W2170299747","https://openalex.org/W2501205181","https://openalex.org/W2525823748","https://openalex.org/W3046457476","https://openalex.org/W4206856450","https://openalex.org/W4210970781","https://openalex.org/W4232495685","https://openalex.org/W4240668518","https://openalex.org/W4241870219","https://openalex.org/W4252104256","https://openalex.org/W4255847471","https://openalex.org/W6607543589","https://openalex.org/W6636091296","https://openalex.org/W6813285973"],"related_works":["https://openalex.org/W4310513842","https://openalex.org/W2020470543","https://openalex.org/W2733910104","https://openalex.org/W4287183010","https://openalex.org/W2963240197","https://openalex.org/W3163480701","https://openalex.org/W4297040228","https://openalex.org/W2000673346","https://openalex.org/W4367684936","https://openalex.org/W3007874878"],"abstract_inverted_index":{"In":[0],"this":[1,116,122],"concluding":[2],"part":[3],"of":[4,7,16,66,87,115,121,124,129],"a":[5,17,37,47,59],"series":[6,123],"papers":[8,125],"on":[9,32,40,49,91],"tetrahedral":[10],"polynomial":[11,18,48],"extension":[12,19,53,80,101],"operators,":[13],"the":[14,22,41,52,69,73,82,85,92,100,119,127],"existence":[15,128],"operator":[20,54,102],"in":[21,72,81],"Sobolev":[23],"space":[24],"$\\boldsymbol":[25,109],"{H}(\\mathrm":[26,110],"{div})$":[27],"is":[28,46,78,103,126],"proven":[29],"constructively.":[30],"Specifically,":[31],"any":[33],"tetrahedron":[34],"$K$,":[35],"given":[36],"function":[38,61,77],"$w$":[39,57],"boundary":[42,93],"$\\partial":[43,94],"K$":[44,95],"that":[45,84],"each":[50],"face,":[51],"applied":[55],"to":[56],"gives":[58],"vector":[60,76],"whose":[62],"components":[63],"are":[64],"polynomials":[65],"at":[67],"most":[68],"same":[70],"degree":[71],"tetrahedron.":[74],"The":[75,112],"an":[79],"sense":[83],"trace":[86],"its":[88],"normal":[89],"component":[90],"coincides":[96],"with":[97,132],"$w$.":[98],"Furthermore,":[99],"continuous":[104],"from":[105],"$H^{-1/2}(\\partial":[106],"K)$":[107],"into":[108],"{div},K)$.":[111],"main":[113],"application":[114],"result":[117],"and":[118],"results":[120],"commuting":[130],"projectors":[131],"good":[133],"$hp$-approximation":[134],"properties.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
