{"id":"https://openalex.org/W2888830273","doi":"https://doi.org/10.1137/18m1210575","title":"$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Navier--Stokes Equations","display_name":"$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Navier--Stokes Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2888830273","doi":"https://doi.org/10.1137/18m1210575","mag":"2888830273"},"language":"en","primary_location":{"id":"doi:10.1137/18m1210575","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1210575","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.10626","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029279895","display_name":"Andrea Beck","orcid":"https://orcid.org/0000-0003-3634-7447"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andrea Beck","raw_affiliation_strings":["Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055177911","display_name":"Jakob D\u00fcrrw\u00e4chter","orcid":"https://orcid.org/0000-0001-8961-5340"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jakob D\u00fcrrw\u00e4chter","raw_affiliation_strings":["Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049832764","display_name":"T. K\u00fchn","orcid":"https://orcid.org/0000-0001-7449-9287"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Kuhn","raw_affiliation_strings":["Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101601724","display_name":"Fabian Meyer","orcid":"https://orcid.org/0000-0001-6603-4121"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Fabian Meyer","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112858542","display_name":"Claus\u2010Dieter Munz","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Claus-Dieter Munz","raw_affiliation_strings":["Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101833555","display_name":"Christian Rohde","orcid":"https://orcid.org/0000-0001-9183-5094"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Rohde","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5101601724"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":0.6808,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74301459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"42","issue":"4","first_page":"B1067","last_page":"B1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"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":0.9993000030517578,"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":0.995199978351593,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6746787428855896},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.6213452816009521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6207929253578186},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.609332799911499},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.5964962244033813},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5403301119804382},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44507041573524475},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4375646114349365},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4168005883693695},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.3552607297897339},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.27422627806663513}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6746787428855896},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.6213452816009521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6207929253578186},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.609332799911499},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.5964962244033813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5403301119804382},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44507041573524475},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4375646114349365},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4168005883693695},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.3552607297897339},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.27422627806663513},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1210575","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1210575","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:arXiv.org:1808.10626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.10626","pdf_url":"https://arxiv.org/pdf/1808.10626","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.10626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.10626","pdf_url":"https://arxiv.org/pdf/1808.10626","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1421374937","display_name":null,"funder_award_id":"BW-HPC2: SEAL","funder_id":"https://openalex.org/F4320310414","funder_display_name":"Baden-W\u00fcrttemberg Stiftung"}],"funders":[{"id":"https://openalex.org/F4320310414","display_name":"Baden-W\u00fcrttemberg Stiftung","ror":"https://ror.org/031h5fa94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1595193945","https://openalex.org/W1835030294","https://openalex.org/W1969915246","https://openalex.org/W1994099903","https://openalex.org/W1998602489","https://openalex.org/W1999469479","https://openalex.org/W2014945091","https://openalex.org/W2024771618","https://openalex.org/W2036766781","https://openalex.org/W2048594685","https://openalex.org/W2069366742","https://openalex.org/W2071518311","https://openalex.org/W2079263908","https://openalex.org/W2102999784","https://openalex.org/W2130342057","https://openalex.org/W2135459060","https://openalex.org/W2163715525","https://openalex.org/W2538426846","https://openalex.org/W2571096229","https://openalex.org/W2746896737","https://openalex.org/W2789683185","https://openalex.org/W2793146214","https://openalex.org/W2889343555","https://openalex.org/W2962953857","https://openalex.org/W2962962060","https://openalex.org/W2964025847","https://openalex.org/W2964293934","https://openalex.org/W3101913164","https://openalex.org/W3103019089"],"related_works":["https://openalex.org/W2089909466","https://openalex.org/W3208000705","https://openalex.org/W2089799198","https://openalex.org/W2126034343","https://openalex.org/W3193597985","https://openalex.org/W2032748140","https://openalex.org/W1032761112","https://openalex.org/W3014952517","https://openalex.org/W2227109165","https://openalex.org/W2392523851"],"abstract_inverted_index":{"We":[0,67,100],"propose":[1,102],"a":[2,48,103,110,147,180],"novel":[3,104],"$hp$-multilevel":[4,75],"Monte":[5,76],"Carlo":[6,77],"method":[7,22,78,130,190],"for":[8,47,114,135,170],"the":[9,14,19,38,42,55,64,70,74,81,89,98,115,157,171,189],"quantification":[10],"of":[11,31,41,52,63,73,92,118,150,160],"uncertainties":[12],"in":[13,54,88,132],"compressible":[15,173],"Navier--Stokes":[16,174],"equations,":[17],"using":[18],"discontinuous":[20],"Galerkin":[21],"as":[23],"deterministic":[24],"solver.":[25],"The":[26,129],"multilevel":[27],"approach":[28,107],"exploits":[29],"hierarchies":[30],"uniformly":[32],"refined":[33],"meshes":[34],"while":[35],"simultaneously":[36],"increasing":[37],"polynomial":[39],"degree":[40],"ansatz":[43],"space.":[44],"It":[45],"allows":[46],"very":[49],"large":[50,148],"range":[51],"resolutions":[53],"physical":[56],"space":[57],"and":[58,105],"thus":[59],"an":[60],"efficient":[61],"decrease":[62],"statistical":[65],"error.":[66],"prove":[68],"that":[69,188],"overall":[71],"complexity":[72],"to":[79,97,108,124,145,193],"compute":[80,146],"mean":[82],"field":[83],"with":[84,95],"prescribed":[85],"accuracy":[86],"is,":[87],"best":[90],"case,":[91],"quadratic":[93],"order":[94],"respect":[96],"accuracy.":[99],"also":[101],"simple":[106],"estimate":[109],"lower":[111],"confidence":[112],"bound":[113],"optimal":[116,158],"number":[117,149,159],"samples":[119,151],"per":[120],"level,":[121],"which":[122],"helps":[123],"prevent":[125],"overestimating":[126,156],"these":[127],"quantities.":[128],"is":[131,143,191],"particular":[133,177],"designed":[134],"application":[136],"on":[137],"queue-based":[138],"computing":[139],"systems,":[140],"where":[141],"it":[142],"desirable":[144],"during":[152],"one":[153],"iteration":[154],"without":[155],"samples.":[161],"Our":[162],"theoretical":[163],"results":[164],"are":[165],"verified":[166],"by":[167],"numerical":[168],"experiments":[169],"two-dimensional":[172],"equations.":[175],"In":[176],"we":[178],"consider":[179],"cavity":[181],"flow":[182],"problem":[183],"from":[184],"computational":[185],"acoustics,":[186],"demonstrating":[187],"suitable":[192],"handle":[194],"complex":[195],"engineering":[196],"problems.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2018-09-07T00:00:00"}
