{"id":"https://openalex.org/W3037124262","doi":"https://doi.org/10.1090/mcom/3572","title":"Robust a posteriori error estimation for parameter-dependent linear elasticity equations","display_name":"Robust a posteriori error estimation for parameter-dependent linear elasticity equations","publication_year":2020,"publication_date":"2020-08-19","ids":{"openalex":"https://openalex.org/W3037124262","doi":"https://doi.org/10.1090/mcom/3572","mag":"3037124262"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3572","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3572","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03572-8/S0025-5718-2020-03572-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03572-8/S0025-5718-2020-03572-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040684079","display_name":"Arbaz Khan","orcid":"https://orcid.org/0000-0001-6625-700X"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Arbaz Khan","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Roorkee (IITR), India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Roorkee (IITR), India","institution_ids":["https://openalex.org/I154851008"]}]},{"author_position":"middle","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, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, United Kingdom","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073050362","display_name":"Catherine E. Powell","orcid":"https://orcid.org/0000-0003-3605-6797"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Catherine E. Powell","raw_affiliation_strings":["School of Mathematics, University of Manchester, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Manchester, United Kingdom","institution_ids":["https://openalex.org/I28407311"]}]},{"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/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David J. Silvester","raw_affiliation_strings":["School of Mathematics, University of Manchester, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Manchester, United Kingdom","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5249,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59814708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"90","issue":"328","first_page":"613","last_page":"636"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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":0.9991999864578247,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8463829755783081},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6085463166236877},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5778452754020691},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.5398127436637878},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.5168828964233398},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4460224509239197},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3397005796432495},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3261301517486572},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20990636944770813}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8463829755783081},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6085463166236877},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5778452754020691},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.5398127436637878},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.5168828964233398},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4460224509239197},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3397005796432495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3261301517486572},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20990636944770813},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3572","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3572","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03572-8/S0025-5718-2020-03572-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/4588d800-f6fb-456b-98a0-9817c064ccd9","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/4588d800-f6fb-456b-98a0-9817c064ccd9","pdf_url":"https://pure.manchester.ac.uk/ws/files/171088067/bkps_aposterioriZ.pdf","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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Khan, A, Bespalov, A, Powell, C & Silvester, D 2020, 'Robust a posteriori error estimation for parameter-dependent linear elasticity equations', Mathematics of Computation, vol. 90, pp. 613-636. https://doi.org/10.1090/mcom/3572","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/fa0957e5-5aca-407d-a26d-ccbe770f03d0","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/fa0957e5-5aca-407d-a26d-ccbe770f03d0","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":"Khan, A, Bespalov, A, Powell, C & Silvester, D 2020, 'Robust a posteriori error estimation for stochastic Galerkin formulations of parameter dependent linear elasticity equations', Mathematics of Computation, vol. 0, 3572. https://doi.org/10.1090/mcom/3572","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/4588d800-f6fb-456b-98a0-9817c064ccd9","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/robust-a-posteriori-error-estimation-for-parameterdependent-linear-elasticity-equations(4588d800-f6fb-456b-98a0-9817c064ccd9).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-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1090/mcom/3572","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3572","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03572-8/S0025-5718-2020-03572-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2221047144","display_name":null,"funder_award_id":"EPSRC grant EP/P013317/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3728093668","display_name":"Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3972664235","display_name":null,"funder_award_id":"EP/P013317","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"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/G4421442999","display_name":null,"funder_award_id":"EP/K032208","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5128091834","display_name":null,"funder_award_id":"EP/K032208/1","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/G6690473478","display_name":null,"funder_award_id":"EP/P013317/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7000731051","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8127123326","display_name":"Numerical analysis of adaptive UQ algorithms for PDEs with random inputs","funder_award_id":"EP/P013317/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3037124262.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W316469091","https://openalex.org/W1538934584","https://openalex.org/W1985422345","https://openalex.org/W1991050908","https://openalex.org/W1991777578","https://openalex.org/W1992591175","https://openalex.org/W1993388225","https://openalex.org/W1995404822","https://openalex.org/W2039412304","https://openalex.org/W2066927514","https://openalex.org/W2083054768","https://openalex.org/W2101552627","https://openalex.org/W2126042051","https://openalex.org/W2133248904","https://openalex.org/W2163739193","https://openalex.org/W2166052342","https://openalex.org/W2270327904","https://openalex.org/W2292462371","https://openalex.org/W2493816570","https://openalex.org/W2505585705","https://openalex.org/W2615439739","https://openalex.org/W2701105359","https://openalex.org/W2794203769","https://openalex.org/W2896629085","https://openalex.org/W2906281376","https://openalex.org/W2963274374","https://openalex.org/W2963604924","https://openalex.org/W2963798430","https://openalex.org/W3013273396","https://openalex.org/W4300004105"],"related_works":["https://openalex.org/W36452949","https://openalex.org/W4319340513","https://openalex.org/W4308705702","https://openalex.org/W2582036733","https://openalex.org/W2012171817","https://openalex.org/W2186661009","https://openalex.org/W2550868073","https://openalex.org/W2950934806","https://openalex.org/W1968392586","https://openalex.org/W2761971374"],"abstract_inverted_index":{"The":[0,19,87,139],"focus":[1],"of":[2,14,38,42,94,118],"this":[3],"work":[4],"is":[5,22,173],"a":[6,23,39,46,55,72,136],"posteriori":[7,73],"error":[8,74,113,133,140],"estimation":[9,75],"for":[10,83,111],"stochastic":[11,63],"Galerkin":[12,64],"approximations":[13],"parameter-dependent":[15],"linear":[16],"elasticity":[17],"equations.":[18],"starting":[20],"point":[21],"three-field":[24],"partial":[25],"differential":[26],"equation":[27],"model":[28],"with":[29,52,116],"the":[30,84,90,95,101,112,119,131,151,161],"Young":[31],"modulus":[32],"represented":[33],"as":[34,98,100],"an":[35,71,125],"affine":[36],"function":[37],"countable":[40],"set":[41],"parameters.":[43,106],"We":[44,69,107],"introduce":[45],"weak":[47],"formulation,":[48],"establish":[49,78],"its":[50,60],"stability":[51],"respect":[53],"to":[54,145,159],"weighted":[56],"norm":[57],"and":[58,77,80,103,122,148],"discuss":[59,109],"approximation":[61,85,120],"using":[62,167],"mixed":[65],"finite":[66],"element":[67],"methods.":[68],"motivate":[70],"scheme":[76],"upper":[79],"lower":[81],"bounds":[82,91],"error.":[86],"constants":[88],"in":[89,150],"are":[92,143,157],"independent":[93],"Poisson":[96],"ratio":[97],"well":[99],"spatial":[102],"parametric":[104],"discretisation":[105],"also":[108],"proxies":[110,142],"reduction":[114,141],"associated":[115],"enrichments":[117],"spaces":[121],"we":[123],"develop":[124],"adaptive":[126],"algorithm":[127],"that":[128,172],"terminates":[129],"when":[130],"estimated":[132],"falls":[134],"below":[135],"user-prescribed":[137],"tolerance.":[138],"shown":[144],"be":[146],"reliable":[147],"efficient":[149],"incompressible":[152],"limit":[153],"case.":[154],"Numerical":[155],"results":[156],"presented":[158],"supplement":[160],"theory.":[162],"All":[163],"experiments":[164],"were":[165],"performed":[166],"open":[168],"source":[169],"(IFISS)":[170],"software":[171],"available":[174],"online.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}