{"id":"https://openalex.org/W2292462371","doi":"https://doi.org/10.1137/15m1027048","title":"Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations","display_name":"Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2292462371","doi":"https://doi.org/10.1137/15m1027048","mag":"2292462371"},"language":"en","primary_location":{"id":"doi:10.1137/15m1027048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1027048","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":true,"oa_status":"green","oa_url":"https://research.birmingham.ac.uk/en/publications/b3d0a589-2b6b-4890-a930-078ca925a482","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081277992","display_name":"Alex Bespalov","orcid":"https://orcid.org/0000-0001-6181-6765"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Bespalov","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK,","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007116796","display_name":"David J. Silvester","orcid":"https://orcid.org/0000-0002-0652-5444"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Silvester","raw_affiliation_strings":["Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4877,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.90610041,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"38","issue":"4","first_page":"A2118","last_page":"A2140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9979000091552734,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9912999868392944,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7337036728858948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6732034087181091},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6210752725601196},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6071282625198364},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6045847535133362},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5243318676948547},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.512764036655426},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5070545673370361},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44960951805114746},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.43573153018951416},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.27873894572257996},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10912537574768066}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7337036728858948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6732034087181091},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6210752725601196},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6071282625198364},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6045847535133362},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5243318676948547},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.512764036655426},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5070545673370361},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44960951805114746},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.43573153018951416},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.27873894572257996},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10912537574768066},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/15m1027048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1027048","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:pure.atira.dk:openaire/1b85b13b-53e4-43d8-80db-0b517e064f16","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/1b85b13b-53e4-43d8-80db-0b517e064f16","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bespalov, A & Silvester, D 2016, 'Efficient adaptive stochastic Galerkin methods for parametric operator equations', SIAM Journal on Scientific Computing, vol. 38, no. 4, pp. A2118-A2140. https://doi.org/10.1137/15M1027048","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2313","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/b3d0a589-2b6b-4890-a930-078ca925a482","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/b3d0a589-2b6b-4890-a930-078ca925a482","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bespalov, A & Silvester, D 2016, 'Efficient adaptive stochastic Galerkin methods for parametric operator equations', SIAM Journal on Scientific Computing, vol. 38, no. 4, pp. A2118\u2013A2140. https://doi.org/10.1137/15M1027048","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/1b85b13b-53e4-43d8-80db-0b517e064f16","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/efficient-adaptive-stochastic-galerkin-methods-for-parametric-operator-equations(1b85b13b-53e4-43d8-80db-0b517e064f16).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.atira.dk:publications/b3d0a589-2b6b-4890-a930-078ca925a482","is_oa":false,"landing_page_url":"https://birmingham.elsevierpure.com/en/publications/b3d0a589-2b6b-4890-a930-078ca925a482","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/b3d0a589-2b6b-4890-a930-078ca925a482","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/b3d0a589-2b6b-4890-a930-078ca925a482","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bespalov, A & Silvester, D 2016, 'Efficient adaptive stochastic Galerkin methods for parametric operator equations', SIAM Journal on Scientific Computing, vol. 38, no. 4, pp. A2118\u2013A2140. https://doi.org/10.1137/15M1027048","raw_type":"article"},"sustainable_development_goals":[{"score":0.8899999856948853,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W174882013","https://openalex.org/W1538934584","https://openalex.org/W1593505867","https://openalex.org/W1963837052","https://openalex.org/W1963971342","https://openalex.org/W1991777578","https://openalex.org/W1995404822","https://openalex.org/W2004814202","https://openalex.org/W2024300082","https://openalex.org/W2025769367","https://openalex.org/W2055460625","https://openalex.org/W2061604462","https://openalex.org/W2083054768","https://openalex.org/W2083754610","https://openalex.org/W2101552627","https://openalex.org/W2139798157","https://openalex.org/W2326704909"],"related_works":["https://openalex.org/W2059318893","https://openalex.org/W2095582735","https://openalex.org/W1965698851","https://openalex.org/W834942123","https://openalex.org/W4232542516","https://openalex.org/W3176637561","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,25,31,56],"concerned":[3],"with":[4,17],"the":[5,44,49,78],"design":[6],"and":[7,58,61],"implementation":[8],"of":[9,48],"efficient":[10],"solution":[11],"algorithms":[12],"for":[13,68],"elliptic":[14],"PDE":[15],"problems":[16],"correlated":[18],"random":[19],"data.":[20],"The":[21,74],"energy":[22,38],"orthogonality":[23],"that":[24,42],"built":[26],"into":[27],"stochastic":[28],"Galerkin":[29],"approximations":[30],"cleverly":[32],"exploited":[33],"to":[34,63],"give":[35],"an":[36,65,70],"innovative":[37],"error":[39,54],"estimation":[40],"strategy":[41],"utilizes":[43],"tensor":[45],"product":[46],"structure":[47],"approximation":[50],"space.":[51],"An":[52],"associated":[53],"estimator":[55],"constructed":[57],"shown":[59],"theoretically":[60],"numerically":[62],"be":[64],"effective":[66],"mechanism":[67],"driving":[69],"adaptive":[71],"refinement":[72],"process.":[73],"codes":[75],"used":[76],"in":[77],"numerical":[79],"studies":[80],"are":[81],"available":[82],"online.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
