{"id":"https://openalex.org/W2467355403","doi":"https://doi.org/10.1137/16m1084882","title":"Convergence Rates for Upwind Schemes with Rough Coefficients","display_name":"Convergence Rates for Upwind Schemes with Rough Coefficients","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2467355403","doi":"https://doi.org/10.1137/16m1084882","mag":"2467355403"},"language":"en","primary_location":{"id":"doi:10.1137/16m1084882","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084882","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1606.09156","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andr\u00e9 Schlichting","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andr\u00e9 Schlichting","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Christian Seis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Seis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2631,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.86255028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"55","issue":"2","first_page":"812","last_page":"840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.5156000256538391,"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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.5156000256538391,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.21809999644756317,"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":0.10300000011920929,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.8294000029563904},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5311999917030334},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5184000134468079},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49630001187324524},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4587000012397766},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4221000075340271},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4009999930858612},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.37950000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8619999885559082},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.8294000029563904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5371999740600586},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5311999917030334},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5184000134468079},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49630001187324524},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4587000012397766},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4496000111103058},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.37950000166893005},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.3716000020503998},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.26460000872612},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1084882","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1084882","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.09156","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.09156","pdf_url":"https://arxiv.org/pdf/1606.09156","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:1606.09156","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.09156","pdf_url":"https://arxiv.org/pdf/1606.09156","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1863894199","https://openalex.org/W1974204760","https://openalex.org/W1978337303","https://openalex.org/W1988946272","https://openalex.org/W1991639740","https://openalex.org/W1999203241","https://openalex.org/W2024343740","https://openalex.org/W2040809598","https://openalex.org/W2052104757","https://openalex.org/W2054083100","https://openalex.org/W2054583986","https://openalex.org/W2068039185","https://openalex.org/W2092394100","https://openalex.org/W2092436849","https://openalex.org/W2096413780","https://openalex.org/W2102955267","https://openalex.org/W2141259506","https://openalex.org/W2315768735"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,98,163],"concerned":[3],"with":[4,136],"the":[5,9,24,27,43,50,57,72,93,103,114,132,159],"numerical":[6],"analysis":[7],"of":[8,56,95,113],"explicit":[10],"upwind":[11,51,115],"finite":[12],"volume":[13],"scheme":[14,52,116],"for":[15,68,71,142],"numerically":[16],"solving":[17],"continuity":[18,73],"equations.":[19],"We":[20,41,130],"are":[21,38],"interested":[22],"in":[23,60,102,151],"case":[25],"where":[26],"advecting":[28],"velocity":[29],"field":[30],"has":[31],"spatial":[32],"Sobolev":[33],"regularity":[34],"and":[35,53,119],"initial":[36,144],"data":[37,145],"merely":[39],"integrable.":[40],"estimate":[42,90],"error":[44],"between":[45],"approximate":[46],"solutions":[47,55],"constructed":[48],"by":[49],"distributional":[54],"continuous":[58],"problem":[59],"a":[61,110],"Kantorovich--Rubinstein":[62],"distance,":[63],"which":[64],"was":[65],"recently":[66],"used":[67],"stability":[69],"estimates":[70],"equation":[74],"[C.":[75],"Seis,":[76],"Ann.":[77],"Inst.":[78],"H.":[79],"Poincar\u00e9":[80],"Anal.":[81],"Non":[82],"Lin\u00e9aire,":[83],"https://doi.org/10.1016/j.anihpc.2017.01.001].":[84],"Restricted":[85],"to":[86],"Cartesian":[87],"meshes,":[88],"our":[89],"shows":[91],"that":[92,139,141,158],"rate":[94,162],"weak":[96,133,160],"convergence":[97,134],"at":[99],"least":[100],"1/2":[101,161],"mesh":[104],"size.":[105],"The":[106,154],"proof":[107],"relies":[108],"on":[109],"probabilistic":[111],"interpretation":[112],"[F.":[117],"Delarue":[118],"F.":[120],"Lagouti\u00e8re,":[121],"Arch.":[122],"Ration.":[123],"Mech.":[124],"Anal.,":[125],"199":[126],"(2011),":[127],"pp.":[128],"229--268].":[129],"complement":[131],"result":[135],"an":[137],"example":[138,156],"illustrates":[140],"rough":[143],"no":[146],"rates":[147],"can":[148],"be":[149],"expected":[150],"strong":[152],"norms.":[153],"same":[155],"suggests":[157],"optimal.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-07-22T00:00:00"}
