{"id":"https://openalex.org/W2053833519","doi":"https://doi.org/10.1137/070697872","title":"Analysis of Numerically Induced Oscillations in Two-Dimensional Finite-Element Shallow-Water Models Part II: Free Planetary Waves","display_name":"Analysis of Numerically Induced Oscillations in Two-Dimensional Finite-Element Shallow-Water Models Part II: Free Planetary Waves","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2053833519","doi":"https://doi.org/10.1137/070697872","mag":"2053833519"},"language":"en","primary_location":{"id":"doi:10.1137/070697872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070697872","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/A5111770287","display_name":"Daniel Y. Le Roux","orcid":"https://orcid.org/0000-0001-8799-5159"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Y. Le Roux","raw_affiliation_strings":["Daniel.LeRoux@mat.ulaval.ca and bpouliot@giref.ulaval.ca#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Daniel.LeRoux@mat.ulaval.ca and bpouliot@giref.ulaval.ca#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028100534","display_name":"Benoit Pouliot","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benoit Pouliot","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0647,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.93440668,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"1971","last_page":"1991"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10159","display_name":"Ionosphere and magnetosphere dynamics","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/spurious-relationship","display_name":"Spurious relationship","score":0.7140005826950073},{"id":"https://openalex.org/keywords/rossby-wave","display_name":"Rossby wave","score":0.7118358016014099},{"id":"https://openalex.org/keywords/dispersion-relation","display_name":"Dispersion relation","score":0.6420106291770935},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5985516905784607},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5920885801315308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5286387205123901},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.519640326499939},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5171586871147156},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"Shallow water equations","score":0.4994988441467285},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4663594961166382},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.45650938153266907},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.4302791953086853},{"id":"https://openalex.org/keywords/phase-velocity","display_name":"Phase velocity","score":0.4181123375892639},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4006957709789276},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3699913024902344},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08396318554878235},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08336034417152405}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.7140005826950073},{"id":"https://openalex.org/C145151356","wikidata":"https://www.wikidata.org/wiki/Q1053589","display_name":"Rossby wave","level":2,"score":0.7118358016014099},{"id":"https://openalex.org/C202579712","wikidata":"https://www.wikidata.org/wiki/Q590051","display_name":"Dispersion relation","level":2,"score":0.6420106291770935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985516905784607},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5920885801315308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5286387205123901},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.519640326499939},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5171586871147156},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.4994988441467285},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4663594961166382},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.45650938153266907},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.4302791953086853},{"id":"https://openalex.org/C26682833","wikidata":"https://www.wikidata.org/wiki/Q13824","display_name":"Phase velocity","level":2,"score":0.4181123375892639},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4006957709789276},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3699913024902344},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08396318554878235},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08336034417152405},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C91586092","wikidata":"https://www.wikidata.org/wiki/Q757520","display_name":"Atmospheric sciences","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070697872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070697872","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1570976541","https://openalex.org/W1966473389","https://openalex.org/W1984596684","https://openalex.org/W1991035358","https://openalex.org/W1992966148","https://openalex.org/W2001149830","https://openalex.org/W2027370888","https://openalex.org/W2035928969","https://openalex.org/W2046900856","https://openalex.org/W2069860858","https://openalex.org/W2073209956","https://openalex.org/W2079497053","https://openalex.org/W2086823102","https://openalex.org/W2093033880","https://openalex.org/W2138252088","https://openalex.org/W2166037769","https://openalex.org/W2176229542","https://openalex.org/W2177646996","https://openalex.org/W4229965994"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W1982872877","https://openalex.org/W2367804606","https://openalex.org/W1991445126","https://openalex.org/W102011404","https://openalex.org/W276665270","https://openalex.org/W1969411884"],"abstract_inverted_index":{"The":[0],"behavior":[1],"of":[2,37,46,61,96,115,131],"planetary":[3],"(Rossby)":[4],"waves":[5,139],"in":[6,112,141],"finite-element":[7,48,53],"numerical":[8],"models":[9],"is":[10,29,73,91],"investigated":[11],"by":[12,57],"using":[13,58],"a":[14,59],"quasi-geostrophic":[15],"approximation":[16],"to":[17,32,41,102,120,135],"the":[18,34,43,47,68,78,87,113,121,124,145],"midlatitude,":[19],"$\\beta$-plane,":[20],"two-dimensional":[21],"linear":[22],"shallow-water":[23],"equations.":[24,128],"A":[25],"dispersion":[26,71,79],"relation":[27,72],"analysis":[28],"employed":[30],"here":[31],"determine":[33],"possible":[35],"occurrence":[36],"spurious":[38,110],"modes":[39],"and":[40,75,77,84,105,109,126],"ascertain":[42],"dispersive/dissipative":[44],"nature":[45],"Galerkin":[49],"mixed":[50,62,97],"formulation.":[51],"Three":[52],"pairs":[54],"are":[55,81,140],"considered":[56],"variety":[60],"interpolation":[63,98],"schemes.":[64],"For":[65],"each":[66],"pair":[67],"frequency":[69],"or":[70],"obtained":[74],"analyzed,":[76],"properties":[80],"compared":[82],"analytically":[83],"graphically":[85],"with":[86,144],"continuous":[88],"case.":[89],"It":[90],"shown":[92],"that":[93],"certain":[94],"choices":[95],"schemes":[99],"may":[100],"lead":[101],"significant":[103],"phase":[104],"group":[106],"velocity":[107],"errors":[108],"solutions":[111,130],"calculation":[114],"slow":[116,137],"Rossby":[117,138],"waves,":[118],"due":[119],"coupling":[122],"between":[123],"momentum":[125],"continuity":[127],"Numerical":[129],"two":[132],"test":[133],"problems":[134],"simulate":[136],"good":[142],"agreement":[143],"analytical":[146],"results.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}