{"id":"https://openalex.org/W2062680215","doi":"https://doi.org/10.1137/10079094x","title":"Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems","display_name":"Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2062680215","doi":"https://doi.org/10.1137/10079094x","mag":"2062680215"},"language":"en","primary_location":{"id":"doi:10.1137/10079094x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10079094x","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/A5103053261","display_name":"Jiangguo Liu","orcid":"https://orcid.org/0000-0002-2188-5157"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jiangguo Liu","raw_affiliation_strings":["liu@math.colostate.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"liu@math.colostate.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103053261"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.689,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.71831181,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"49","issue":"5","first_page":"2165","last_page":"2181"},"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":1.0,"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":1.0,"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/T10514","display_name":"Numerical methods in engineering","score":0.9984999895095825,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7945001721382141},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.744705855846405},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7394372820854187},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7314935922622681},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6972776651382446},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.6198358535766602},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.613382875919342},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.576535701751709},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5395604372024536},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.490925133228302},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.46015408635139465},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.4596400558948517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3857194185256958},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12384384870529175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7945001721382141},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.744705855846405},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7394372820854187},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7314935922622681},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6972776651382446},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.6198358535766602},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.613382875919342},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.576535701751709},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5395604372024536},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.490925133228302},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.46015408635139465},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4596400558948517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3857194185256958},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12384384870529175},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/10079094x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10079094x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1967863240","https://openalex.org/W1973545521","https://openalex.org/W2012541063","https://openalex.org/W2035543412","https://openalex.org/W2037332128","https://openalex.org/W2052632666","https://openalex.org/W2058549403","https://openalex.org/W2069951215","https://openalex.org/W2075501190","https://openalex.org/W2083944749","https://openalex.org/W2085488187","https://openalex.org/W2085830137","https://openalex.org/W2086256304","https://openalex.org/W2093922796","https://openalex.org/W2148849010"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W177285201","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"two":[3],"new":[4,56],"finite":[5,25],"element":[6],"methods":[7,13,57],"for":[8,33,46],"two-dimensional":[9],"Stokes":[10],"problems.":[11],"These":[12,55],"are":[14,29,53,58,70],"developed":[15],"by":[16],"relaxing":[17],"the":[18,21,38,51,74],"constraints":[19],"of":[20,35],"Crouzeix\u2013Raviart":[22],"nonconforming":[23],"$P_1$":[24],"elements.":[26],"Penalty":[27],"terms":[28],"introduced":[30],"to":[31,60,72],"compensate":[32],"lack":[34],"continuity":[36],"or":[37],"divergence-free":[39],"property.":[40],"However,":[41],"there":[42],"is":[43],"no":[44],"need":[45],"choosing":[47],"penalty":[48],"factors,":[49],"and":[50,62],"formulations":[52],"symmetric.":[54],"easy":[59],"implement":[61],"avoid":[63],"solving":[64],"saddle-point":[65],"linear":[66],"systems.":[67],"Numerical":[68],"experiments":[69],"presented":[71],"illustrate":[73],"proved":[75],"optimal":[76],"error":[77],"estimates.":[78]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
