{"id":"https://openalex.org/W2054034220","doi":"https://doi.org/10.1137/050646421","title":"An Augmented Lagrangian\u2010Based Approach to the Oseen Problem","display_name":"An Augmented Lagrangian\u2010Based Approach to the Oseen Problem","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2054034220","doi":"https://doi.org/10.1137/050646421","mag":"2054034220"},"language":"en","primary_location":{"id":"doi:10.1137/050646421","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646421","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["Emory University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077985757","display_name":"Maxim A. Olshanskii","orcid":"https://orcid.org/0000-0002-9102-6833"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maxim A. Olshanskii","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6488,"has_fulltext":false,"cited_by_count":258,"citation_normalized_percentile":{"value":0.97824366,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"28","issue":"6","first_page":"2095","last_page":"2113"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/preconditioner","display_name":"Preconditioner","score":0.9286724328994751},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.7153201103210449},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.7093230485916138},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6965651512145996},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6661562323570251},{"id":"https://openalex.org/keywords/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.6601783633232117},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6579675674438477},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5704227089881897},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.48612141609191895},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4478491544723511},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4320582449436188},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3901122808456421},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.341025710105896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24931266903877258},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.24066442251205444},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1474601924419403}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9286724328994751},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.7153201103210449},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.7093230485916138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6965651512145996},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6661562323570251},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.6601783633232117},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6579675674438477},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5704227089881897},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.48612141609191895},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4478491544723511},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4320582449436188},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3901122808456421},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.341025710105896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24931266903877258},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.24066442251205444},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1474601924419403},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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":3,"locations":[{"id":"doi:10.1137/050646421","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646421","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.6383","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.6383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mathcs.emory.edu/~benzi/Web_papers/OseenAL.pdf","raw_type":"text"},{"id":"pmh:oai:ricerca.sns.it:11384/75228","is_oa":false,"landing_page_url":"http://hdl.handle.net/11384/75228","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W609598071","https://openalex.org/W841836366","https://openalex.org/W1487997876","https://openalex.org/W1524324710","https://openalex.org/W1560263223","https://openalex.org/W1852082788","https://openalex.org/W1963751327","https://openalex.org/W1967011851","https://openalex.org/W1969605668","https://openalex.org/W1972148882","https://openalex.org/W1974461496","https://openalex.org/W1988719701","https://openalex.org/W1993077381","https://openalex.org/W2017085690","https://openalex.org/W2021116964","https://openalex.org/W2037818443","https://openalex.org/W2042004309","https://openalex.org/W2048752392","https://openalex.org/W2052158395","https://openalex.org/W2053295724","https://openalex.org/W2053994227","https://openalex.org/W2060732875","https://openalex.org/W2073897969","https://openalex.org/W2075194837","https://openalex.org/W2076972307","https://openalex.org/W2077658674","https://openalex.org/W2081523040","https://openalex.org/W2082606496","https://openalex.org/W2099359799","https://openalex.org/W2120749833","https://openalex.org/W2121613024","https://openalex.org/W2127190985","https://openalex.org/W2133248904","https://openalex.org/W2134528122","https://openalex.org/W2137086911","https://openalex.org/W2141870784","https://openalex.org/W2148028437","https://openalex.org/W2155216327","https://openalex.org/W2802365918","https://openalex.org/W3012317737","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W4286903191","https://openalex.org/W4389317411","https://openalex.org/W2617415041","https://openalex.org/W4286902343","https://openalex.org/W2566317144","https://openalex.org/W1492522302","https://openalex.org/W2096454229","https://openalex.org/W1567048268","https://openalex.org/W2042199958","https://openalex.org/W3046775784"],"abstract_inverted_index":{"We":[0,84,100],"describe":[1],"an":[2,12],"effective":[3],"solver":[4],"for":[5,46,57,88],"the":[6,17,47,75,82,112],"discrete":[7],"Oseen":[8],"problem":[9],"based":[10],"on":[11],"augmented":[13],"Lagrangian":[14],"formulation":[15],"of":[16,74,97,104,114],"corresponding":[18],"saddle":[19],"point":[20],"system.":[21],"The":[22,38],"proposed":[23],"method":[24],"is":[25,41],"a":[26,32,42,52,105],"block":[27],"triangular":[28],"preconditioner":[29],"used":[30],"with":[31,107],"Krylov":[33],"subspace":[34],"iteration":[35],"like":[36],"BiCGStab.":[37],"crucial":[39],"ingredient":[40],"novel":[43],"multigrid":[44],"approach":[45,68],"(1,1)":[48],"block,":[49],"which":[50],"extends":[51],"technique":[53],"introduced":[54],"by":[55],"Schoberl":[56],"elasticity":[58],"problems":[59],"to":[60,81],"nonsymmetric":[61],"problems.":[62],"Our":[63],"analysis":[64],"indicates":[65],"that":[66],"this":[67],"results":[69,103],"in":[70,95],"fast":[71],"convergence,":[72],"independent":[73],"mesh":[76],"size":[77],"and":[78,91],"largely":[79],"insensitive":[80],"viscosity.":[83],"present":[85],"experimental":[86],"evidence":[87],"both":[89],"isoP2\u2010P0":[90],"isoP2\u2010P1":[92],"finite":[93],"elements":[94],"support":[96],"our":[98,115],"conclusions.":[99],"also":[101],"show":[102],"comparison":[106],"two":[108],"state\u2010of\u2010the\u2010art":[109],"preconditioners,":[110],"showing":[111],"competitiveness":[113],"approach.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":13}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}