{"id":"https://openalex.org/W2069366742","doi":"https://doi.org/10.1090/s0025-5718-2012-02574-9","title":"Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data","display_name":"Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data","publication_year":2012,"publication_date":"2012-04-05","ids":{"openalex":"https://openalex.org/W2069366742","doi":"https://doi.org/10.1090/s0025-5718-2012-02574-9","mag":"2069366742"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02574-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02574-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02574-9/S0025-5718-2012-02574-9.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/2012-81-280/S0025-5718-2012-02574-9/S0025-5718-2012-02574-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105583288","display_name":"S. Mishra","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"S. Mishra","raw_affiliation_strings":["Seminar for Applied Mathematics, ETH, HG G. 57.2, R\u00c3\u00a4mistrasse 101, Z\u00c3\u00bcrich, Switzerland","Seminar for Applied Mathematics, ETH, HG G. 57.2, R\u00e4mistrasse 101, Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH, HG G. 57.2, R\u00c3\u00a4mistrasse 101, Z\u00c3\u00bcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH, HG G. 57.2, R\u00e4mistrasse 101, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110826197","display_name":"Ch. Schwab","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ch. Schwab","raw_affiliation_strings":["Seminar for Applied Mathematics, ETH, HG G. 57.1, R\u00c3\u00a4mistrasse 101, Z\u00c3\u00bcrich, Switzerland","Seminar for Applied Mathematics, ETH, HG G. 57.1, R\u00e4mistrasse 101, Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH, HG G. 57.1, R\u00c3\u00a4mistrasse 101, Z\u00c3\u00bcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH, HG G. 57.1, R\u00e4mistrasse 101, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5105583288"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":12.0007,"has_fulltext":true,"cited_by_count":149,"citation_normalized_percentile":{"value":0.99100856,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"81","issue":"280","first_page":"1979","last_page":"2018"},"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":0.9923999905586243,"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":0.9923999905586243,"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":0.9907000064849854,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.6388324499130249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4169521927833557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4091149866580963}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6388324499130249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4169521927833557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4091149866580963}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02574-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02574-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02574-9/S0025-5718-2012-02574-9.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02574-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02574-9","pdf_url":"https://www.ams.org/mcom/2012-81-280/S0025-5718-2012-02574-9/S0025-5718-2012-02574-9.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":[{"score":0.6600000262260437,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069366742.pdf","grobid_xml":"https://content.openalex.org/works/W2069366742.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W654155693","https://openalex.org/W1531416578","https://openalex.org/W1542004730","https://openalex.org/W1549748890","https://openalex.org/W1571871558","https://openalex.org/W1595775464","https://openalex.org/W1835030294","https://openalex.org/W1982867713","https://openalex.org/W1990592929","https://openalex.org/W2007024093","https://openalex.org/W2008874036","https://openalex.org/W2036766781","https://openalex.org/W2038991247","https://openalex.org/W2051553803","https://openalex.org/W2053576040","https://openalex.org/W2064517598","https://openalex.org/W2065588677","https://openalex.org/W2094582224","https://openalex.org/W2117358914","https://openalex.org/W2142678007","https://openalex.org/W2163715525","https://openalex.org/W2251490743","https://openalex.org/W2481459718","https://openalex.org/W2490550871","https://openalex.org/W2733965690","https://openalex.org/W2739334789","https://openalex.org/W4205438089","https://openalex.org/W4237689332","https://openalex.org/W4292081050","https://openalex.org/W4292367709","https://openalex.org/W4300475775"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0,32,76],"consider":[1],"scalar":[2],"hyperbolic":[3],"conservation":[4],"laws":[5],"in":[6],"spatial":[7],"dimension":[8],"<inline-formula":[9,59,108],"content-type=\"math/mathml\">":[10,60,109],"<mml:math":[11,61,110],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,62,111],"alttext=\"d":[13],"greater-than-or-equal-to":[14],"1\">":[15],"<mml:semantics>":[16,64,113],"<mml:mrow>":[17],"<mml:mi>d</mml:mi>":[18],"<mml:mo>\u2265</mml:mo>":[19],"<mml:mn>1</mml:mn>":[20],"</mml:mrow>":[21],"<mml:annotation":[22,66,115],"encoding=\"application/x-tex\">d\\geq":[23],"1</mml:annotation>":[24],"</mml:semantics>":[25,68,117],"</mml:math>":[26,69,118],"</inline-formula>":[27,70],"with":[28],"stochastic":[29],"initial":[30,47],"data.":[31],"prove":[33],"existence":[34,52],"and":[35,41],"uniqueness":[36],"of":[37,53,56,71,80,83,94,98,106,139,154,164],"a":[38,78,136],"random-entropy":[39],"solution":[40],"give":[42],"sufficient":[43],"conditions":[44],"on":[45],"the":[46,51,92,95,99,129,140,145,152],"data":[48],"that":[49],"ensure":[50],"statistical":[54,162],"moments":[55,163],"any":[57],"order":[58],"alttext=\"k\">":[63,112],"<mml:mi>k</mml:mi>":[65,114],"encoding=\"application/x-tex\">k</mml:annotation>":[67,116],"this":[72],"random":[73,100],"entropy":[74,101],"solution.":[75],"present":[77],"class":[79],"numerical":[81],"schemes":[82,124,156],"multi-level":[84],"Monte":[85],"Carlo":[86],"Finite":[87],"Volume":[88],"(MLMC-FVM)":[89],"type":[90],"for":[91,144],"approximation":[93],"ensemble":[96],"average":[97],"solutions":[102,166],"as":[103,105,135],"well":[104],"their":[107],"</inline-formula>-point":[119],"space-time":[120],"correlation":[121],"functions.":[122],"These":[123],"are":[125,157,167],"shown":[126],"to":[127,169],"obey":[128],"same":[130],"accuracy":[131],"vs.":[132],"work":[133],"estimate":[134],"single":[137],"application":[138],"finite":[141],"volume":[142],"solver":[143],"corresponding":[146],"deterministic":[147],"problem.":[148],"Numerical":[149],"experiments":[150],"demonstrating":[151],"efficiency":[153],"these":[155],"presented.":[158],"In":[159],"certain":[160],"cases,":[161],"discontinuous":[165],"found":[168],"be":[170],"more":[171],"regular":[172],"than":[173],"pathwise":[174],"solutions.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":6}],"updated_date":"2026-01-17T23:10:49.606395","created_date":"2025-10-10T00:00:00"}