{"id":"https://openalex.org/W1985432921","doi":"https://doi.org/10.1090/s0025-5718-08-02130-3","title":"Local projection stabilization of equal order interpolation applied to the Stokes problem","display_name":"Local projection stabilization of equal order interpolation applied to the Stokes problem","publication_year":2008,"publication_date":"2008-05-09","ids":{"openalex":"https://openalex.org/W1985432921","doi":"https://doi.org/10.1090/s0025-5718-08-02130-3","mag":"1985432921"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02130-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02130-3","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02130-3/S0025-5718-08-02130-3.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/2008-77-264/S0025-5718-08-02130-3/S0025-5718-08-02130-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082244505","display_name":"Sashikumaar Ganesan","orcid":"https://orcid.org/0000-0003-1858-3972"},"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":"Sashikumaar Ganesan","raw_affiliation_strings":["Institut f\u00c3\u00bcr Analysis und Numerik, Otto-von-Guericke-Universit\u00c3\u00a4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","Institut f\u00fcr Analysis und Numerik, Otto-von-Guericke Universit\u00e4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Analysis und Numerik, Otto-von-Guericke-Universit\u00c3\u00a4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Numerik, Otto-von-Guericke Universit\u00e4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany#TAB#","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041040975","display_name":"Gunar Matthies","orcid":"https://orcid.org/0000-0002-9476-3740"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gunar Matthies","raw_affiliation_strings":["Fakult\u00c3\u00a4t f\u00c3\u00bcr Mathematik, Ruhr-Universit\u00c3\u00a4t Bochum, Universit\u00c3\u00a4tsstrasse 150, D-44780 Bochum, Germany","Fakultat fur Mathematik, Ruhr-Universitat Bochum, Universitatsstrasse 150, D-44780, Bochum, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00c3\u00a4t f\u00c3\u00bcr Mathematik, Ruhr-Universit\u00c3\u00a4t Bochum, Universit\u00c3\u00a4tsstrasse 150, D-44780 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"Fakultat fur Mathematik, Ruhr-Universitat Bochum, Universitatsstrasse 150, D-44780, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"last","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":["Institut f\u00c3\u00bcr Analysis und Numerik, Otto-von-Guericke-Universit\u00c3\u00a4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","Institut f\u00fcr Analysis und Numerik, Otto-von-Guericke Universit\u00e4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Analysis und Numerik, Otto-von-Guericke-Universit\u00c3\u00a4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Numerik, Otto-von-Guericke Universit\u00e4t Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany#TAB#","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082244505"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":null,"apc_paid":null,"fwci":8.4273,"has_fulltext":true,"cited_by_count":69,"citation_normalized_percentile":{"value":0.98225086,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"77","issue":"264","first_page":"2039","last_page":"2060"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8476501703262329},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7496914863586426},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7399648427963257},{"id":"https://openalex.org/keywords/stencil","display_name":"Stencil","score":0.7367269992828369},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.6685599684715271},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6238871812820435},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6001555919647217},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.5773760080337524},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5336927175521851},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4961718022823334},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.433206707239151},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41716134548187256},{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.4129977822303772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4100215435028076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28239506483078003},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26096272468566895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08593380451202393},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.05948662757873535}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8476501703262329},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7496914863586426},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7399648427963257},{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.7367269992828369},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.6685599684715271},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6238871812820435},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6001555919647217},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.5773760080337524},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5336927175521851},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4961718022823334},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.433206707239151},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41716134548187256},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.4129977822303772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4100215435028076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28239506483078003},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26096272468566895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08593380451202393},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.05948662757873535},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-08-02130-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02130-3","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02130-3/S0025-5718-08-02130-3.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/s0025-5718-08-02130-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02130-3","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02130-3/S0025-5718-08-02130-3.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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985432921.pdf","grobid_xml":"https://content.openalex.org/works/W1985432921.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W40469006","https://openalex.org/W74678517","https://openalex.org/W125509687","https://openalex.org/W1525538887","https://openalex.org/W1603384270","https://openalex.org/W1674659126","https://openalex.org/W1778185943","https://openalex.org/W1852082788","https://openalex.org/W1967538702","https://openalex.org/W1972368368","https://openalex.org/W1974461496","https://openalex.org/W1986608219","https://openalex.org/W1990392133","https://openalex.org/W2009985306","https://openalex.org/W2023754092","https://openalex.org/W2039259138","https://openalex.org/W2041523977","https://openalex.org/W2041563881","https://openalex.org/W2049914863","https://openalex.org/W2051984102","https://openalex.org/W2066090268","https://openalex.org/W2068845153","https://openalex.org/W2084209794","https://openalex.org/W2091914394","https://openalex.org/W2095399846","https://openalex.org/W2124268718","https://openalex.org/W2151030709","https://openalex.org/W2158856246","https://openalex.org/W2165940086","https://openalex.org/W2199169705","https://openalex.org/W2289366489","https://openalex.org/W2934526567","https://openalex.org/W2974351797","https://openalex.org/W3149667697","https://openalex.org/W4205634890","https://openalex.org/W4238156215","https://openalex.org/W4242522383","https://openalex.org/W4245007249","https://openalex.org/W6605310286","https://openalex.org/W6631567118"],"related_works":["https://openalex.org/W1968086293","https://openalex.org/W2119558010","https://openalex.org/W2062207398","https://openalex.org/W2056063496","https://openalex.org/W246128123","https://openalex.org/W2023838565","https://openalex.org/W1993770029","https://openalex.org/W2082741444","https://openalex.org/W774881382","https://openalex.org/W2393270639"],"abstract_inverted_index":{"The":[0,22,100],"local":[1,52],"projection":[2,23,53,65,83],"stabilization":[3,54,136],"allows":[4],"us":[5],"to":[6,12,115,133],"circumvent":[7],"the":[8,19,33,69,104,124,134],"Babu\u00c5\u00a1ka\u00e2\u0080\u0093Brezzi":[9],"condition":[10],"and":[11,63,82,96],"use":[13],"equal":[14],"order":[15,73],"interpolation":[16],"for":[17,78],"discretizing":[18],"Stokes":[20],"problem.":[21],"is":[24,76,113],"usually":[25],"done":[26],"in":[27,117],"a":[28,37,44,50,86],"two-level":[29],"approach":[30,102],"by":[31],"projecting":[32],"pressure":[34],"gradient":[35],"onto":[36],"discontinuous":[38,64],"finite":[39,60,94],"element":[40,61],"space":[41],"living":[42],"on":[43,57,68],"patch":[45],"of":[46,74,80,106],"elements.":[47,99],"We":[48],"propose":[49],"new":[51,101],"method":[55],"based":[56],"(possibly)":[58],"enriched":[59,92],"spaces":[62,66,84],"defined":[67],"same":[70],"mesh.":[71],"Optimal":[72],"convergence":[75,126],"shown":[77],"pairs":[79],"approximation":[81],"satisfying":[85],"certain":[87],"inf-sup":[88],"condition.":[89],"Examples":[90],"are":[91,129],"simplicial":[93],"elements":[95],"standard":[97],"quadrilateral/hexahedral":[98],"overcomes":[103],"problem":[105],"an":[107],"increasing":[108],"discretization":[109],"stencil":[110],"and,":[111],"thus,":[112],"simple":[114],"implement":[116],"existing":[118],"computer":[119],"codes.":[120],"Numerical":[121],"tests":[122],"confirm":[123],"theoretical":[125],"results":[127],"which":[128],"robust":[130],"with":[131],"respect":[132],"user-chosen":[135],"parameter.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}