{"id":"https://openalex.org/W3200509021","doi":"https://doi.org/10.1137/20m1342586","title":"Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method","display_name":"Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3200509021","doi":"https://doi.org/10.1137/20m1342586","mag":"3200509021"},"language":"en","primary_location":{"id":"doi:10.1137/20m1342586","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1342586","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://epubs.siam.org/doi/10.1137/20M1342586","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":"middle","author":{"id":"https://openalex.org/A5022125095","display_name":"Dirk Praetorius","orcid":"https://orcid.org/0000-0002-1977-9830"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Dirk Praetorius","raw_affiliation_strings":["Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-1977-9830","affiliations":[{"raw_affiliation_string":"Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059625967","display_name":"Michele Ruggeri","orcid":"https://orcid.org/0000-0001-6213-1602"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Michele Ruggeri","raw_affiliation_strings":["Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0001-6213-1602","affiliations":[{"raw_affiliation_string":"Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5712,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71793374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"9","issue":"3","first_page":"1184","last_page":"1216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9993000030517578,"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":0.9950000047683716,"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7482957243919373},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7107243537902832},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6502931118011475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5666558146476746},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.5579050183296204},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5265370011329651},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.42643916606903076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39140254259109497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3654383420944214},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.09885740280151367},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08650219440460205}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7482957243919373},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7107243537902832},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6502931118011475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5666558146476746},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.5579050183296204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5265370011329651},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.42643916606903076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39140254259109497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3654383420944214},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.09885740280151367},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08650219440460205},{"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/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1342586","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1342586","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:79759","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/1378929.html>","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":"Article"},{"id":"pmh:oai:cris.unibo.it:11585/944119","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/10.1137/20M1342586","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:publications/775c1ae4-ef0c-4bee-a8c9-f2a31282f5d3","is_oa":false,"landing_page_url":null,"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:cris.unibo.it:11585/944119","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/10.1137/20M1342586","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1309768829","display_name":null,"funder_award_id":"EP/N510129/1.","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G1633672591","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2568532592","display_name":"Taming Complexity in Partial Differential Systems","funder_award_id":"F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3855435662","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G396319395","display_name":"Computational nonlinear PDEs","funder_award_id":"P 33216","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4240251267","display_name":null,"funder_award_id":"EP/P013791/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G444630160","display_name":null,"funder_award_id":"EP/N510129/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4500485203","display_name":"The Alan Turing Institute","funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5580360526","display_name":"Numerical analysis of adaptive UQ algorithms for PDEs with random inputs","funder_award_id":"EP/P013791/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8597009950","display_name":null,"funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1690316246","https://openalex.org/W1828419635","https://openalex.org/W1939142429","https://openalex.org/W1969402876","https://openalex.org/W1982559793","https://openalex.org/W1991777578","https://openalex.org/W2024016211","https://openalex.org/W2024300082","https://openalex.org/W2026409663","https://openalex.org/W2039924562","https://openalex.org/W2044959876","https://openalex.org/W2048791667","https://openalex.org/W2049222546","https://openalex.org/W2057748983","https://openalex.org/W2069379427","https://openalex.org/W2072205359","https://openalex.org/W2082051696","https://openalex.org/W2082617508","https://openalex.org/W2083754610","https://openalex.org/W2094400909","https://openalex.org/W2101552627","https://openalex.org/W2102031020","https://openalex.org/W2126980197","https://openalex.org/W2135459060","https://openalex.org/W2292462371","https://openalex.org/W2558873235","https://openalex.org/W2794203769","https://openalex.org/W2799041766","https://openalex.org/W2805831676","https://openalex.org/W2884465099","https://openalex.org/W2900922842","https://openalex.org/W2956240439","https://openalex.org/W2963604924","https://openalex.org/W2964025847","https://openalex.org/W3013273396","https://openalex.org/W3021245493","https://openalex.org/W3021293439","https://openalex.org/W3036306518","https://openalex.org/W3037484550","https://openalex.org/W3038337385","https://openalex.org/W3098592456","https://openalex.org/W3100356286","https://openalex.org/W3102639848","https://openalex.org/W3103499934"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642"],"abstract_inverted_index":{"The":[0,100],"paper":[1,101],"considers":[2],"a":[3,28,30,57,72],"class":[4,45],"of":[5,46,86,106],"parametric":[6,98],"elliptic":[7],"partial":[8],"differential":[9],"equations":[10],"(PDEs),":[11],"where":[12,83],"the":[13,16,35,52,61,66,84,87],"coefficients":[14],"and":[15,77],"right-hand":[17],"side":[18],"function":[19],"depend":[20],"on":[21],"infinitely":[22],"many":[23],"(uncertain)":[24],"parameters.":[25],"We":[26,49,75],"introduce":[27],"two-level":[29,53],"posteriori":[31],"estimator":[32,54,88],"to":[33,71,91],"control":[34],"energy":[36],"error":[37],"in":[38],"multilevel":[39,108],"stochastic":[40,109],"Galerkin":[41,110],"approximations":[42],"for":[43,60],"this":[44],"PDE":[47],"problems.":[48],"prove":[50],"that":[51],"always":[55],"provides":[56],"lower":[58],"bound":[59,68],"unknown":[62],"approximation":[63],"error,":[64],"while":[65],"upper":[67],"is":[69,89],"equivalent":[70],"saturation":[73],"assumption.":[74],"propose":[76],"empirically":[78],"compare":[79],"three":[80],"adaptive":[81],"algorithms,":[82],"structure":[85],"exploited":[90],"perform":[92],"spatial":[93],"refinement":[94],"as":[95,97],"well":[96],"enrichment.":[99],"also":[102],"discusses":[103],"implementation":[104],"aspects":[105],"computing":[107],"approximations.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
