{"id":"https://openalex.org/W1975977317","doi":"https://doi.org/10.1137/11082539x","title":"Bernstein\u2013B\u00e9zier Finite Elements of Arbitrary Order and Optimal Assembly Procedures","display_name":"Bernstein\u2013B\u00e9zier Finite Elements of Arbitrary Order and Optimal Assembly Procedures","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1975977317","doi":"https://doi.org/10.1137/11082539x","mag":"1975977317"},"language":"en","primary_location":{"id":"doi:10.1137/11082539x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082539x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":["M.Ainsworth@strath.ac.uk and gaelle.andriamaro@strath.ac.uk and oleg.davydov@ strath.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"M.Ainsworth@strath.ac.uk and gaelle.andriamaro@strath.ac.uk and oleg.davydov@ strath.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088898753","display_name":"Ga\u00eblle Andriamaro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gaelle Andriamaro","raw_affiliation_strings":["Mathematics And Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064667546","display_name":"Oleg Davydov","orcid":"https://orcid.org/0000-0001-8813-9485"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oleg Davydov","raw_affiliation_strings":["Mathematics And Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.6355,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.97906966,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"6","first_page":"3087","last_page":"3109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T10221","display_name":"Composite Structure Analysis and Optimization","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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9980999827384949,"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":0.8368042707443237},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7004920244216919},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6868091821670532},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6437690258026123},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.5497808456420898},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4586179256439209},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.43935760855674744},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.43575870990753174},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.4137512445449829},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3779289126396179},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3487086296081543},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.334469735622406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31094977259635925},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14671564102172852}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8368042707443237},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7004920244216919},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6868091821670532},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6437690258026123},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.5497808456420898},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4586179256439209},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.43935760855674744},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.43575870990753174},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.4137512445449829},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3779289126396179},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3487086296081543},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.334469735622406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31094977259635925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14671564102172852},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/11082539x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082539x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:36314","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/36314/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1976584147","https://openalex.org/W1980005758","https://openalex.org/W1985144286","https://openalex.org/W2004993896","https://openalex.org/W2011212378","https://openalex.org/W2024136494","https://openalex.org/W2050066249","https://openalex.org/W2057627929","https://openalex.org/W2062660733","https://openalex.org/W2102076631","https://openalex.org/W2127570421","https://openalex.org/W2135723931","https://openalex.org/W2153731524","https://openalex.org/W2154281337"],"related_works":["https://openalex.org/W1997494471","https://openalex.org/W2281104490","https://openalex.org/W2194207844","https://openalex.org/W1994950933","https://openalex.org/W2603457763","https://openalex.org/W2097504581","https://openalex.org/W2002088832","https://openalex.org/W2969628250","https://openalex.org/W2953297366","https://openalex.org/W2964223321"],"abstract_inverted_index":{"Algorithms":[0],"are":[1,43,74,80],"presented":[2],"that":[3],"enable":[4],"the":[5,9,81,88],"element":[6,12,91],"matrices":[7],"for":[8,87],"standard":[10,89],"finite":[11,90],"space,":[13],"consisting":[14],"of":[15,19,58],"continuous":[16],"piecewise":[17],"polynomials":[18,78],"degree":[20],"n":[21],"on":[22,53,76,93],"simplicial":[23,94],"elements":[24,73],"in":[25,30],"$\\mathbb{R}^d$,":[26],"to":[27,45,83],"be":[28,68],"computed":[29],"optimal":[31,85],"complexity":[32,86],"$\\mathcal{O}(n^{2d})$.":[33],"The":[34,72],"algorithms":[35],"(i)":[36],"take":[37],"into":[38],"account":[39],"numerical":[40],"quadrature;":[41],"(ii)":[42],"applicable":[44],"nonlinear":[46],"problems;":[47],"and":[48,79],"(iii)":[49],"do":[50],"not":[51],"rely":[52],"precomputed":[54],"arrays":[55],"containing":[56],"values":[57],"one-dimensional":[59],"basis":[60],"functions":[61],"at":[62],"quadrature":[63],"points":[64],"(although":[65],"these":[66],"can":[67],"used":[69],"if":[70],"desired).":[71],"based":[75],"Bernstein":[77],"first":[82],"achieve":[84],"spaces":[92],"elements.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}