{"id":"https://openalex.org/W1977714802","doi":"https://doi.org/10.1090/s0025-5718-00-01239-4","title":"Simple finite element method in vorticity formulation for incompressible flows","display_name":"Simple finite element method in vorticity formulation for incompressible flows","publication_year":2000,"publication_date":"2000-03-03","ids":{"openalex":"https://openalex.org/W1977714802","doi":"https://doi.org/10.1090/s0025-5718-00-01239-4","mag":"1977714802"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01239-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01239-4","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01239-4/S0025-5718-00-01239-4.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/2001-70-234/S0025-5718-00-01239-4/S0025-5718-00-01239-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019169169","display_name":"Jian\u2010Guo Liu","orcid":"https://orcid.org/0000-0002-9911-4045"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jian-Guo Liu","raw_affiliation_strings":["Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742","University of Maryland, College Park"],"affiliations":[{"raw_affiliation_string":"Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071854504","display_name":"E Weinan","orcid":"https://orcid.org/0000-0003-0272-9500"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weinan E","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York, NY 10012","New York University"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York, NY 10012","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019169169"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":2.7707,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.88383376,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"70","issue":"234","first_page":"579","last_page":"593"},"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":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9980000257492065,"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/finite-element-method","display_name":"Finite element method","score":0.8152148723602295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7789543867111206},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.6973018050193787},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.688134491443634},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.6573657393455505},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.6483441591262817},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.636384904384613},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6323429346084595},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.5788476467132568},{"id":"https://openalex.org/keywords/smoothed-finite-element-method","display_name":"Smoothed finite element method","score":0.5679106116294861},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.49114128947257996},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.4788793921470642},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.460085391998291},{"id":"https://openalex.org/keywords/finite-element-limit-analysis","display_name":"Finite element limit analysis","score":0.4487234950065613},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.405517041683197},{"id":"https://openalex.org/keywords/boundary-knot-method","display_name":"Boundary knot method","score":0.33803465962409973},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2499012053012848},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.20910167694091797},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.20099782943725586},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.16023573279380798},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10733175277709961},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.04358583688735962}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8152148723602295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7789543867111206},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.6973018050193787},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.688134491443634},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.6573657393455505},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.6483441591262817},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.636384904384613},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6323429346084595},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.5788476467132568},{"id":"https://openalex.org/C177605945","wikidata":"https://www.wikidata.org/wiki/Q11007230","display_name":"Smoothed finite element method","level":5,"score":0.5679106116294861},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.49114128947257996},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4788793921470642},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.460085391998291},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.4487234950065613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.405517041683197},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.33803465962409973},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2499012053012848},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.20910167694091797},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.20099782943725586},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.16023573279380798},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10733175277709961},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.04358583688735962},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-00-01239-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01239-4","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01239-4/S0025-5718-00-01239-4.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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.7585","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.7585","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01239-4/S0025-5718-00-01239-4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.8494","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.8494","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~jliu/research/pdf/SFEM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.8511","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.8511","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~jliu/research/psfiles/SFEM.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.95.385","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.385","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.princeton.edu/~weinan/pdf files/simple.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01239-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01239-4","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01239-4/S0025-5718-00-01239-4.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":[],"awards":[{"id":"https://openalex.org/G1131208725","display_name":"Efficient Numerical Methods for Unsteady Viscous            Incompressible Flows","funder_award_id":"9805621","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1977714802.pdf","grobid_xml":"https://content.openalex.org/works/W1977714802.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1037752369","https://openalex.org/W1521454588","https://openalex.org/W1580847363","https://openalex.org/W1634938045","https://openalex.org/W1674659126","https://openalex.org/W1775501378","https://openalex.org/W1994912872","https://openalex.org/W2006332168","https://openalex.org/W2008693023","https://openalex.org/W2017916357","https://openalex.org/W2030525496","https://openalex.org/W2036138588","https://openalex.org/W2041523977","https://openalex.org/W2043683510","https://openalex.org/W2061170279","https://openalex.org/W2067109487","https://openalex.org/W2096727598","https://openalex.org/W2121815894","https://openalex.org/W2166590326","https://openalex.org/W2168452607","https://openalex.org/W3149667697","https://openalex.org/W4251180451","https://openalex.org/W4255628612"],"related_works":["https://openalex.org/W1989473560","https://openalex.org/W1977906733","https://openalex.org/W1031178128","https://openalex.org/W2048691789","https://openalex.org/W1567939749","https://openalex.org/W2565231037","https://openalex.org/W1998844869","https://openalex.org/W1972557980","https://openalex.org/W165701716","https://openalex.org/W2376732695"],"abstract_inverted_index":{"A":[0],"very":[1],"simple":[2],"and":[3,12,70],"efficient":[4],"finite":[5,29,40,60],"element":[6,30,61],"method":[7,23,31,66],"is":[8,67,71],"introduced":[9,43],"for":[10,74],"two":[11],"three":[13],"dimensional":[14],"viscous":[15],"incompressible":[16],"flows":[17],"using":[18,58],"the":[19,27,33,36,45],"vorticity":[20],"formulation.":[21],"This":[22],"relies":[24],"on":[25],"recasting":[26],"traditional":[28],"in":[32,47],"spirit":[34],"of":[35,52],"high":[37,77],"order":[38,54],"accurate":[39],"difference":[41],"methods":[42],"by":[44],"authors":[46],"another":[48],"work.":[49],"Optimal":[50],"accuracy":[51],"arbitrary":[53],"can":[55],"be":[56],"achieved":[57],"standard":[59],"or":[62],"spectral":[63],"elements.":[64],"The":[65],"convectively":[68],"stable":[69],"particularly":[72],"suited":[73],"moderate":[75],"to":[76],"Reynolds":[78],"number":[79],"flows.":[80]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
