{"id":"https://openalex.org/W2924040522","doi":"https://doi.org/10.1137/090780122","title":"An \"$hp$\" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations","display_name":"An \"$hp$\" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2924040522","doi":"https://doi.org/10.1137/090780122","mag":"2924040522"},"language":"en","primary_location":{"id":"doi:10.1137/090780122","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090780122","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/A5006481666","display_name":"Jens L. Eftang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jens L. Eftang","raw_affiliation_strings":["Department of Mathematical Sciences,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences,","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063350067","display_name":"Anthony T. Patera","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Anthony T. Patera","raw_affiliation_strings":["Department of Mechanical Engineering, MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, MIT","institution_ids":["https://openalex.org/I4210109586"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064491960","display_name":"Einar M. R\u00f8nquist","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Einar M. R\u00f8nquist","raw_affiliation_strings":["Department of Mathematical Sciences, NTNU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, NTNU","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0064,"has_fulltext":false,"cited_by_count":176,"citation_normalized_percentile":{"value":0.97740911,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"32","issue":"6","first_page":"3170","last_page":"3200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7405071258544922},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.578697919845581},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5709089636802673},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5211719870567322},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.48332953453063965},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4771951138973236},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4573665261268616},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4443662762641907},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4322056770324707},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.4225006699562073},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3782583475112915},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3259866237640381},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2870703339576721},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09339603781700134},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08653303980827332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7405071258544922},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.578697919845581},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5709089636802673},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5211719870567322},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.48332953453063965},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4771951138973236},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4573665261268616},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4443662762641907},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4322056770324707},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.4225006699562073},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3782583475112915},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3259866237640381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2870703339576721},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09339603781700134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08653303980827332},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090780122","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090780122","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4099999964237213,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311040","display_name":"Norges Teknisk-Naturvitenskapelige Universitet","ror":"https://ror.org/05xg72x27"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1486369067","https://openalex.org/W1633869374","https://openalex.org/W1967011851","https://openalex.org/W1976653974","https://openalex.org/W1977681898","https://openalex.org/W1978588246","https://openalex.org/W1983500141","https://openalex.org/W1987070389","https://openalex.org/W2003207029","https://openalex.org/W2032768921","https://openalex.org/W2042426282","https://openalex.org/W2044498528","https://openalex.org/W2047591100","https://openalex.org/W2052690618","https://openalex.org/W2080556931","https://openalex.org/W2091917844","https://openalex.org/W2100143228","https://openalex.org/W2104225554","https://openalex.org/W2110917150","https://openalex.org/W2120433265","https://openalex.org/W2122080931","https://openalex.org/W2124236693","https://openalex.org/W2155257515","https://openalex.org/W2156425660","https://openalex.org/W2161024376","https://openalex.org/W2168970443","https://openalex.org/W2243394101","https://openalex.org/W2316290730"],"related_works":["https://openalex.org/W2682190590","https://openalex.org/W2358589552","https://openalex.org/W4366197524","https://openalex.org/W935007796","https://openalex.org/W2027741235","https://openalex.org/W2066764747","https://openalex.org/W2079390358","https://openalex.org/W1533062418","https://openalex.org/W1974193032","https://openalex.org/W1994929327"],"abstract_inverted_index":{"We":[0,28,106],"present":[1,107],"a":[2,35,52,88,112],"new":[3,36,104,116],"\u201c$hp$\u201d":[4],"parameter":[5,44,48,57,65,84],"multidomain":[6],"certified":[7],"reduced":[8,128],"basis":[9,129],"(RB)":[10],"method":[11,130],"for":[12,38,111],"rapid":[13],"and":[14,30,87,99],"reliable":[15],"online":[16,133],"evaluation":[17],"of":[18,42,55,102],"functional":[19],"outputs":[20],"associated":[21],"with":[22],"parametrized":[23],"elliptic":[24],"partial":[25],"differential":[26],"equations.":[27],"propose,":[29],"provide":[31],"theoretical":[32],"justification":[33],"for,":[34],"procedure":[37],"adaptive":[39],"partition":[40],"(\u201ch\u201d-refinement)":[41],"the":[43,56,97,103,115,125,132],"domain":[45],"into":[46],"smaller":[47],"subdomains:":[49],"we":[50,72],"pursue":[51],"hierarchical":[53],"splitting":[54],"(sub)domains":[58],"based":[59],"on":[60],"proximity":[61],"to":[62],"judiciously":[63],"chosen":[64],"anchor":[66],"points":[67],"within":[68],"each":[69,81],"subdomain.":[70,82],"Subsequently,":[71],"construct":[73],"individual":[74],"standard":[75,126],"RB":[76],"approximation":[77],"spaces":[78],"(\u201cp\u201d-refinement)":[79],"over":[80],"Greedy":[83],"sampling":[85],"procedures":[86],"posteriori":[89],"error":[90],"estimation":[91],"play":[92],"important":[93],"roles":[94],"in":[95,131],"both":[96],"\u201ch\u201d-type":[98],"\u201cp\u201d-type":[100,127],"stages":[101],"algorithm.":[105],"illustrative":[108],"numerical":[109],"results":[110],"convection-diffusion":[113],"problem:":[114],"\u201c$hp$\u201d-approach":[117],"is":[118],"considerably":[119],"faster":[120],"(respectively,":[121,134],"more":[122],"costly)":[123],"than":[124],"offline)":[135],"stage.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-30T13:55:48.251075","created_date":"2025-10-10T00:00:00"}