{"id":"https://openalex.org/W2045765566","doi":"https://doi.org/10.1137/100809519","title":"Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages","display_name":"Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2045765566","doi":"https://doi.org/10.1137/100809519","mag":"2045765566"},"language":"en","primary_location":{"id":"doi:10.1137/100809519","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100809519","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://discovery.ucl.ac.uk/1384725/1/Burman_SISC_BBT11.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064837569","display_name":"Malte Braack","orcid":"https://orcid.org/0000-0003-1730-6316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Braack","raw_affiliation_strings":["braack@math.uni-kiel.de and taschenberger@math.uni-kiel.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"braack@math.uni-kiel.de and taschenberger@math.uni-kiel.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011409848","display_name":"Erik Burman","orcid":"https://orcid.org/0000-0003-4287-7241"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Burman","raw_affiliation_strings":["erik.burman@sussex.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"erik.burman@sussex.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079582852","display_name":"Nico Taschenberger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Taschenberger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4663,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.88333333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"5","first_page":"2199","last_page":"2216"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9987000226974487,"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":0.9984999895095825,"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":0.8600051403045654},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6548320055007935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6123304963111877},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6094774007797241},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5717280507087708},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5348339080810547},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5346009135246277},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5064069032669067},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.46432963013648987},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4608679711818695},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3798277974128723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3542434573173523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16739842295646667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8600051403045654},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6548320055007935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6123304963111877},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6094774007797241},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5717280507087708},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5348339080810547},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5346009135246277},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5064069032669067},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.46432963013648987},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4608679711818695},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3798277974128723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3542434573173523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16739842295646667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100809519","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100809519","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:eprints.ucl.ac.uk.OAI2:1384725","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1384725/","pdf_url":"https://discovery.ucl.ac.uk/1384725/1/Burman_SISC_BBT11.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM Journal on Scientific Computing , 33  (5)   2199 - 2216.   (2011)      ","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1384725","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1384725/","pdf_url":"https://discovery.ucl.ac.uk/1384725/1/Burman_SISC_BBT11.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM Journal on Scientific Computing , 33  (5)   2199 - 2216.   (2011)      ","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2045765566.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1998967184","https://openalex.org/W2045956558","https://openalex.org/W2050721148","https://openalex.org/W2064588031","https://openalex.org/W2093572013","https://openalex.org/W2104616000","https://openalex.org/W2105593012","https://openalex.org/W2133147107","https://openalex.org/W2358129718"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W2560215812","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2954004777","https://openalex.org/W1480770706","https://openalex.org/W3042022377"],"abstract_inverted_index":{"We":[0,44],"propose":[1],"an":[2,61,75],"a":[3,32,38,70,103,131],"posteriori":[4],"error":[5,78],"estimation":[6],"technique":[7,92],"for":[8,16,127],"the":[9,49,84,93,112,123,137],"computation":[10],"of":[11,14,51,60,83],"average":[12],"functionals":[13],"solutions":[15],"nonlinear":[17],"time":[18,53],"dependent":[19,54],"problems":[20],"based":[21],"on":[22],"duality":[23],"techniques.":[24],"The":[25,57],"exact":[26,110,118],"solution":[27],"is":[28,97],"assumed":[29],"to":[30,47,89,99,122,135],"have":[31],"periodic":[33],"or":[34],"quasi-periodic":[35],"behavior":[36],"favoring":[37],"fixed":[39],"mesh":[40],"strategy":[41],"in":[42,133],"time.":[43],"show":[45],"how":[46],"circumvent":[48],"need":[50],"solving":[52],"dual":[55,72],"problems.":[56],"estimator":[58],"consists":[59],"averaged":[62],"residual":[63],"weighted":[64],"by":[65],"sensitivity":[66],"factors":[67],"coming":[68,80],"from":[69,81],"stationary":[71],"problem":[73,107,126],"and":[74,120],"additional":[76],"averaging":[77],"term":[79],"nonlinearities":[82],"operator":[85],"considered.":[86],"In":[87],"order":[88,134],"illustrate":[90],"this":[91],"resulting":[94],"adaptive":[95],"algorithm":[96],"applied":[98],"several":[100],"model":[101],"problems:":[102],"linear":[104],"scalar":[105],"parabolic":[106],"with":[108,116],"known":[109,117],"solution,":[111,119],"nonsteady":[113],"Navier\u2013Stokes":[114,128],"equations":[115],"finally":[121],"well-known":[124],"benchmark":[125],"(flow":[129],"behind":[130],"cylinder)":[132],"verify":[136],"modeling":[138],"assumptions.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}