{"id":"https://openalex.org/W2028916079","doi":"https://doi.org/10.1137/060651227","title":"An Energy- and Helicity-Conserving Finite Element Scheme for the Navier\u2013Stokes Equations","display_name":"An Energy- and Helicity-Conserving Finite Element Scheme for the Navier\u2013Stokes Equations","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2028916079","doi":"https://doi.org/10.1137/060651227","mag":"2028916079"},"language":"en","primary_location":{"id":"doi:10.1137/060651227","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651227","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/A5028355904","display_name":"Leo G. Rebholz","orcid":"https://orcid.org/0000-0002-5173-5731"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Leo G. Rebholz","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028355904"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7009,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.94510688,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"4","first_page":"1622","last_page":"1638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994000196456909,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9965999722480774,"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":0.7926738262176514},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7513371706008911},{"id":"https://openalex.org/keywords/helicity","display_name":"Helicity","score":0.7197471261024475},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5883411169052124},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.5568959712982178},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5289932489395142},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.5286688804626465},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5146278142929077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5068512558937073},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4814971685409546},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46128007769584656},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.433050274848938},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25385940074920654},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.21890556812286377},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1446039378643036},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.10299938917160034},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.10058724880218506}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7926738262176514},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7513371706008911},{"id":"https://openalex.org/C2775859700","wikidata":"https://www.wikidata.org/wiki/Q568855","display_name":"Helicity","level":2,"score":0.7197471261024475},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5883411169052124},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.5568959712982178},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5289932489395142},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.5286688804626465},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5146278142929077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5068512558937073},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4814971685409546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46128007769584656},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.433050274848938},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25385940074920654},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.21890556812286377},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1446039378643036},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.10299938917160034},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.10058724880218506},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060651227","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651227","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:CiteSeerX.psu:10.1.1.140.1056","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.1056","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.pitt.edu/techrep/0602.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1988243598","https://openalex.org/W1992935563","https://openalex.org/W1999195967","https://openalex.org/W2029463917","https://openalex.org/W2033492814","https://openalex.org/W2051862019","https://openalex.org/W2053562573","https://openalex.org/W2073256259","https://openalex.org/W2076582418","https://openalex.org/W2083953196","https://openalex.org/W2099803355","https://openalex.org/W2130686389","https://openalex.org/W2165891499","https://openalex.org/W3204708751","https://openalex.org/W4251401595"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2792440356","https://openalex.org/W3112745479","https://openalex.org/W4378474062","https://openalex.org/W4210855719","https://openalex.org/W1658046627","https://openalex.org/W2058384118"],"abstract_inverted_index":{"We":[0,32],"present":[1],"a":[2,50,70,74],"new":[3],"finite":[4],"element":[5],"scheme":[6,85],"for":[7,39,66],"solving":[8,65],"the":[9,25,40,53,58,62,84,87],"Navier\u2013Stokes":[10],"equations":[11],"that":[12,82],"exactly":[13,46],"conserves":[14],"both":[15,67],"energy":[16],"$(\\int_{\\Omega}u^{2})$":[17],"and":[18,29,37,43,64,69],"helicity":[19,44],"$(\\int_{\\Omega}":[20],"u\\cdot(\\nabla":[21],"\\times":[22],"u))$":[23],"in":[24,73],"absence":[26],"of":[27,52,61],"viscosity":[28],"external":[30],"force.":[31],"prove":[33],"stability,":[34],"exact":[35],"conservation,":[36],"convergence":[38],"scheme.":[41],"Energy":[42],"are":[45,80],"conserved":[47],"by":[48],"using":[49],"combination":[51],"usual":[54,88],"(convective)":[55],"form":[56,60],"with":[57],"rotational":[59],"nonlinearity":[63],"velocity":[68],"projected":[71],"vorticity":[72],"trapezoidal":[75,89],"time":[76],"discretization.":[77],"Numerical":[78],"results":[79],"presented":[81],"compare":[83],"to":[86],"schemes.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}