{"id":"https://openalex.org/W2344397854","doi":"https://doi.org/10.1137/151006196","title":"A High-Order, Analytically Divergence-Free Approximation Method for the Time-Dependent Stokes Problem","display_name":"A High-Order, Analytically Divergence-Free Approximation Method for the Time-Dependent Stokes Problem","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2344397854","doi":"https://doi.org/10.1137/151006196","mag":"2344397854"},"language":"en","primary_location":{"id":"doi:10.1137/151006196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006196","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004812364","display_name":"Christopher Keim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher Keim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066096555","display_name":"Holger Wendland","orcid":"https://orcid.org/0000-0002-9614-5321"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Holger Wendland","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004812364"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2862,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.56897861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"2","first_page":"1288","last_page":"1312"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9973000288009644,"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/mathematics","display_name":"Mathematics","score":0.8252251148223877},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7191253900527954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5669223070144653},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.540499210357666},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4937504231929779},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.46533527970314026},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4442659616470337},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4408615827560425},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4404262602329254},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.431363582611084},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42323964834213257},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4166485369205475},{"id":"https://openalex.org/keywords/moving-least-squares","display_name":"Moving least squares","score":0.41552338004112244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36734452843666077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.242817223072052},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.15934127569198608},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13719594478607178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10652709007263184}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252251148223877},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7191253900527954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5669223070144653},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.540499210357666},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4937504231929779},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.46533527970314026},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4442659616470337},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4408615827560425},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4404262602329254},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.431363582611084},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42323964834213257},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4166485369205475},{"id":"https://openalex.org/C2780580100","wikidata":"https://www.wikidata.org/wiki/Q6927143","display_name":"Moving least squares","level":2,"score":0.41552338004112244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36734452843666077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.242817223072052},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.15934127569198608},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13719594478607178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10652709007263184},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"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/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/151006196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151006196","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::55245","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:eref.uni-bayreuth.de:55245","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/55245/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7842179496","display_name":null,"funder_award_id":"WE 2333/8-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W104736067","https://openalex.org/W112187595","https://openalex.org/W144669444","https://openalex.org/W1968682790","https://openalex.org/W1986280275","https://openalex.org/W1990554393","https://openalex.org/W1993831627","https://openalex.org/W1996243745","https://openalex.org/W1997488868","https://openalex.org/W2000068428","https://openalex.org/W2002199481","https://openalex.org/W2005632248","https://openalex.org/W2010122118","https://openalex.org/W2011290221","https://openalex.org/W2012300893","https://openalex.org/W2017940249","https://openalex.org/W2021218667","https://openalex.org/W2024119359","https://openalex.org/W2031178557","https://openalex.org/W2035637093","https://openalex.org/W2036326859","https://openalex.org/W2039744571","https://openalex.org/W2040747006","https://openalex.org/W2047877145","https://openalex.org/W2051661029","https://openalex.org/W2056782393","https://openalex.org/W2060244959","https://openalex.org/W2068527585","https://openalex.org/W2080356937","https://openalex.org/W2087243319","https://openalex.org/W2087928860","https://openalex.org/W2100675673","https://openalex.org/W2102483543","https://openalex.org/W2118922968","https://openalex.org/W2127689830","https://openalex.org/W2146589365","https://openalex.org/W2150612352","https://openalex.org/W2153320359","https://openalex.org/W2161591817","https://openalex.org/W2166050051","https://openalex.org/W2315257963","https://openalex.org/W3133571595","https://openalex.org/W4231163017","https://openalex.org/W4241834112","https://openalex.org/W4244807417"],"related_works":["https://openalex.org/W2370840338","https://openalex.org/W2388641108","https://openalex.org/W2368317224","https://openalex.org/W2370651559","https://openalex.org/W2383177152","https://openalex.org/W3000893075","https://openalex.org/W2263321684","https://openalex.org/W2008932759","https://openalex.org/W2045907273","https://openalex.org/W2781988545"],"abstract_inverted_index":{"We":[0,32,113],"develop":[1],"and":[2,90],"analyze":[3],"a":[4,19,28,47,116],"new":[5],"high-order":[6],"approximation":[7,36,44],"method":[8,15,121,132],"for":[9],"the":[10,24,58,68,72,78,120,123,131],"time-dependent":[11],"Stokes":[12,25],"equation.":[13,31],"Our":[14],"is":[16,60,74,111],"based":[17],"upon":[18],"Leray":[20],"projection,":[21],"which":[22],"converts":[23],"equation":[26],"into":[27],"vector-valued":[29],"heat":[30],"then":[33],"employ":[34],"meshfree":[35],"spaces":[37,45],"to":[38,87,97],"discretize":[39],"in":[40,105,122,136],"space.":[41],"These":[42],"discrete":[43],"use":[46,103],"well-chosen":[48],"pair":[49],"of":[50,71,119],"matrix-valued":[51],"kernels":[52],"such":[53],"that,":[54],"among":[55],"other":[56],"things,":[57],"velocity":[59],"approximated":[61],"by":[62],"an":[63],"analytically":[64],"divergence-free":[65],"function.":[66],"Moreover,":[67],"pressure":[69],"part":[70],"solution":[73],"computed":[75],"simultaneously":[76],"with":[77],"velocity,":[79],"so":[80,91],"that":[81,92],"no":[82,93,107],"additional":[83],"auxiliary":[84],"problem":[85],"has":[86],"be":[88,98,134],"solved":[89],"inf-sup":[94],"conditions":[95],"have":[96],"satisfied.":[99],"Finally,":[100],"since":[101],"we":[102],"collocation":[104],"space,":[106],"spatial":[108],"numerical":[109],"integration":[110],"required.":[112],"will":[114],"give":[115],"rigorous":[117],"analysis":[118],"periodic":[124],"setting":[125],"but":[126],"also":[127],"point":[128],"out":[129],"how":[130],"can":[133],"used":[135],"more":[137],"general":[138],"situations.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
