{"id":"https://openalex.org/W2971401012","doi":"https://doi.org/10.1007/s00211-019-01097-9","title":"Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis","display_name":"Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis","publication_year":2020,"publication_date":"2020-01-29","ids":{"openalex":"https://openalex.org/W2971401012","doi":"https://doi.org/10.1007/s00211-019-01097-9","mag":"2971401012"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-019-01097-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-019-01097-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.03559","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Espen Sande","orcid":null},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Espen Sande","raw_affiliation_strings":["Department of Mathematics, University of Rome Tor Vergata, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rome Tor Vergata, Rome, Italy","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Carla Manni","orcid":null},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carla Manni","raw_affiliation_strings":["Department of Mathematics, University of Rome Tor Vergata, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rome Tor Vergata, Rome, Italy","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hendrik Speleers","orcid":null},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Hendrik Speleers","raw_affiliation_strings":["Department of Mathematics, University of Rome Tor Vergata, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rome Tor Vergata, Rome, Italy","institution_ids":["https://openalex.org/I116067653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I116067653"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.1259,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.95026509,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"144","issue":"4","first_page":"889","last_page":"929"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9731000065803528,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9731000065803528,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0017000000225380063,"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":0.0015999999595806003,"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/spline","display_name":"Spline (mechanical)","score":0.8482000231742859},{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.7716000080108643},{"id":"https://openalex.org/keywords/hermite-spline","display_name":"Hermite spline","score":0.7167999744415283},{"id":"https://openalex.org/keywords/m-spline","display_name":"M-spline","score":0.6179999709129333},{"id":"https://openalex.org/keywords/smoothing-spline","display_name":"Smoothing spline","score":0.608299970626831},{"id":"https://openalex.org/keywords/perfect-spline","display_name":"Perfect spline","score":0.5839999914169312},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.5788999795913696},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5277000069618225},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5113999843597412}],"concepts":[{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.8482000231742859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8355000019073486},{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.7716000080108643},{"id":"https://openalex.org/C186763157","wikidata":"https://www.wikidata.org/wiki/Q5741918","display_name":"Hermite spline","level":5,"score":0.7167999744415283},{"id":"https://openalex.org/C199765470","wikidata":"https://www.wikidata.org/wiki/Q6712116","display_name":"M-spline","level":5,"score":0.6179999709129333},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.608299970626831},{"id":"https://openalex.org/C205224112","wikidata":"https://www.wikidata.org/wiki/Q4426180","display_name":"Perfect spline","level":5,"score":0.5839999914169312},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.5788999795913696},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5277000069618225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5259000062942505},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5113999843597412},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5051000118255615},{"id":"https://openalex.org/C120742014","wikidata":"https://www.wikidata.org/wiki/Q7226491","display_name":"Polyharmonic spline","level":5,"score":0.4846999943256378},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.46399998664855957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4611000120639801},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.35530000925064087},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.2565999925136566},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-019-01097-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-019-01097-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.03559","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.03559","pdf_url":"https://arxiv.org/pdf/1909.03559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:art.torvergata.it:2108/253370","is_oa":false,"landing_page_url":"http://hdl.handle.net/2108/253370","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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":{"id":"pmh:oai:arXiv.org:1909.03559","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.03559","pdf_url":"https://arxiv.org/pdf/1909.03559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1862031973","https://openalex.org/W2001440251","https://openalex.org/W2065189656","https://openalex.org/W2074623661","https://openalex.org/W2082771977","https://openalex.org/W2085827032","https://openalex.org/W2101402782","https://openalex.org/W2123417665","https://openalex.org/W2479456404","https://openalex.org/W2560948221","https://openalex.org/W2753048319","https://openalex.org/W2756397932","https://openalex.org/W2786668430","https://openalex.org/W2889857442","https://openalex.org/W2890142970","https://openalex.org/W2898917727","https://openalex.org/W2964999402","https://openalex.org/W4212799367","https://openalex.org/W4230104359","https://openalex.org/W4237713727","https://openalex.org/W4299521717"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-09-12T00:00:00"}