{"id":"https://openalex.org/W1992075486","doi":"https://doi.org/10.1090/s0025-5718-2010-02404-4","title":"Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes Problem","display_name":"Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes Problem","publication_year":2010,"publication_date":"2010-12-29","ids":{"openalex":"https://openalex.org/W1992075486","doi":"https://doi.org/10.1090/s0025-5718-2010-02404-4","mag":"1992075486"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2010-02404-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02404-4","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02404-4/S0025-5718-2010-02404-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02404-4/S0025-5718-2010-02404-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004566181","display_name":"Hagen Eichel","orcid":null},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hagen Eichel","raw_affiliation_strings":["Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053874836","display_name":"Lutz Tobiska","orcid":null},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz Tobiska","raw_affiliation_strings":["Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052078853","display_name":"Hehu Xie","orcid":"https://orcid.org/0000-0002-1947-9256"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Hehu Xie","raw_affiliation_strings":["Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China"],"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004566181"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":null,"apc_paid":null,"fwci":0.692,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.7116467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"274","first_page":"697","last_page":"697"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965999722480774,"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/superconvergence","display_name":"Superconvergence","score":0.9955759048461914},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.8460307717323303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8062196969985962},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7993464469909668},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7511985301971436},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6168088912963867},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5565198659896851},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5471413135528564},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5430620908737183},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5120208859443665},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46515852212905884},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.4651101231575012},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4603860378265381},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43724849820137024},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29421180486679077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12582683563232422},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.06718462705612183},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05578908324241638}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9955759048461914},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.8460307717323303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8062196969985962},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7993464469909668},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7511985301971436},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6168088912963867},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5565198659896851},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5471413135528564},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5430620908737183},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5120208859443665},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46515852212905884},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.4651101231575012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4603860378265381},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43724849820137024},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29421180486679077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12582683563232422},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.06718462705612183},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05578908324241638},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2010-02404-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02404-4","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02404-4/S0025-5718-2010-02404-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2010-02404-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02404-4","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02404-4/S0025-5718-2010-02404-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.41999998688697815,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G5168466499","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"}],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320326970","display_name":"State Key Laboratory of Scientific and Engineering Computing","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1992075486.pdf","grobid_xml":"https://content.openalex.org/works/W1992075486.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W58679925","https://openalex.org/W125509687","https://openalex.org/W617279438","https://openalex.org/W1595515622","https://openalex.org/W1598588703","https://openalex.org/W1674659126","https://openalex.org/W1778185943","https://openalex.org/W1852082788","https://openalex.org/W1972368368","https://openalex.org/W1984813553","https://openalex.org/W1985207620","https://openalex.org/W1985432921","https://openalex.org/W1986608219","https://openalex.org/W2009478656","https://openalex.org/W2009985306","https://openalex.org/W2016966935","https://openalex.org/W2019461312","https://openalex.org/W2023754092","https://openalex.org/W2030479060","https://openalex.org/W2033868307","https://openalex.org/W2041523977","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2049914863","https://openalex.org/W2050178911","https://openalex.org/W2051984102","https://openalex.org/W2061937382","https://openalex.org/W2065479689","https://openalex.org/W2066090268","https://openalex.org/W2077801576","https://openalex.org/W2084209794","https://openalex.org/W2091156165","https://openalex.org/W2095399846","https://openalex.org/W2124268718","https://openalex.org/W2155395549","https://openalex.org/W2158856246","https://openalex.org/W2289366489","https://openalex.org/W2314717817","https://openalex.org/W2381246980","https://openalex.org/W2974351797","https://openalex.org/W3149667697","https://openalex.org/W4245007249","https://openalex.org/W4252104256","https://openalex.org/W6600263792","https://openalex.org/W6602604683","https://openalex.org/W6605023316","https://openalex.org/W6606002120","https://openalex.org/W6631567118"],"related_works":["https://openalex.org/W2001758285","https://openalex.org/W2737775198","https://openalex.org/W2070923604","https://openalex.org/W2386448237","https://openalex.org/W1992075486","https://openalex.org/W2003775670","https://openalex.org/W2016966935","https://openalex.org/W2351677040","https://openalex.org/W2022473750","https://openalex.org/W190788963"],"abstract_inverted_index":{"The":[0,56],"supercloseness":[1,39,59],"and":[2,66],"superconvergence":[3,89],"properties":[4],"of":[5,40,44],"stabilized":[6],"finite":[7],"element":[8],"methods":[9,23],"applied":[10],"to":[11,36,72,83],"the":[12,38,41,45,84,94],"Stokes":[13],"problem":[14],"are":[15,34,76],"studied.":[16],"We":[17],"consider":[18],"consistent":[19],"residual":[20],"based":[21],"stabilization":[22],"as":[24,26],"well":[25],"inconsistent":[27],"local":[28],"projection":[29],"type":[30],"stabilizations.":[31],"Moreover,":[32],"we":[33,87],"able":[35],"show":[37],"linear":[42],"part":[43],"MINI-element":[46],"solution":[47],"which":[48],"has":[49],"been":[50],"previously":[51],"observed":[52],"in":[53],"practical":[54],"computations.":[55],"results":[57],"on":[58,61],"hold":[60],"three-directional":[62],"triangular,":[63],"axiparallel":[64],"rectangular,":[65],"brick-type":[67],"meshes,":[68],"respectively,":[69],"but":[70],"extensions":[71],"more":[73],"general":[74],"meshes":[75],"also":[77],"discussed.":[78],"Applying":[79],"an":[80],"appropriate":[81],"postprocess":[82],"computed":[85],"solution,":[86],"establish":[88],"results.":[90],"Numerical":[91],"examples":[92],"illustrate":[93],"theoretical":[95],"predictions.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}