{"id":"https://openalex.org/W1966473389","doi":"https://doi.org/10.1137/030602435","title":"Dispersion Relation Analysis of the $P^NC_1 - P^_1$ Finite-Element Pair in Shallow-Water Models","display_name":"Dispersion Relation Analysis of the $P^NC_1 - P^_1$ Finite-Element Pair in Shallow-Water Models","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1966473389","doi":"https://doi.org/10.1137/030602435","mag":"1966473389"},"language":"en","primary_location":{"id":"doi:10.1137/030602435","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602435","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":true,"raw_author_name":"Daniel Y. Le Roux","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5111770287"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1198,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.95240808,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"2","first_page":"394","last_page":"414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11757","display_name":"Seismic Waves and Analysis","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"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/T11757","display_name":"Seismic Waves and Analysis","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6579875349998474},{"id":"https://openalex.org/keywords/dispersion-relation","display_name":"Dispersion relation","score":0.6447211503982544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5952768325805664},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5910203456878662},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5257939696311951},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.49622398614883423},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.47918474674224854},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4641408324241638},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.44462552666664124},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4320446848869324},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38577955961227417},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31044304370880127},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.28684261441230774},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.10119250416755676}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6579875349998474},{"id":"https://openalex.org/C202579712","wikidata":"https://www.wikidata.org/wiki/Q590051","display_name":"Dispersion relation","level":2,"score":0.6447211503982544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5952768325805664},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5910203456878662},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5257939696311951},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.49622398614883423},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.47918474674224854},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4641408324241638},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.44462552666664124},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4320446848869324},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38577955961227417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31044304370880127},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.28684261441230774},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10119250416755676},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/030602435","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602435","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":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W618110921","https://openalex.org/W1570976541","https://openalex.org/W1976217016","https://openalex.org/W1984596684","https://openalex.org/W1985469018","https://openalex.org/W1986608219","https://openalex.org/W2016681772","https://openalex.org/W2019433779","https://openalex.org/W2027370888","https://openalex.org/W2031433022","https://openalex.org/W2045928814","https://openalex.org/W2047658976","https://openalex.org/W2054629935","https://openalex.org/W2055883962","https://openalex.org/W2067392615","https://openalex.org/W2074885630","https://openalex.org/W2076969971","https://openalex.org/W2080790839","https://openalex.org/W2085612505","https://openalex.org/W2085759042","https://openalex.org/W2093033880","https://openalex.org/W2093657229","https://openalex.org/W2138252088","https://openalex.org/W2139013563","https://openalex.org/W2147362949","https://openalex.org/W2166037769","https://openalex.org/W2176229542","https://openalex.org/W3149667697","https://openalex.org/W4231394311","https://openalex.org/W4247875894"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W3134374554","https://openalex.org/W2237480245","https://openalex.org/W2519167559","https://openalex.org/W2075065631","https://openalex.org/W2167473861","https://openalex.org/W2069347647"],"abstract_inverted_index":{"Shallow-water":[0],"models":[1],"typically":[2],"employ":[3],"gridpoint,":[4],"finite,":[5],"and":[6,19,26,47,64,93,117,128,151,160],"spectral-element":[7],"techniques.":[8],"For":[9],"most":[10],"of":[11,35,45,52,67,89,119,140,167],"these":[12],"methods":[13],"the":[14,17,33,50,70,87,90,115,132,136,141,147,158,165,168],"coupling":[15],"between":[16],"momentum":[18],"continuity":[20],"equations":[21],"is":[22,82,95],"a":[23,42,98,125],"delicate":[24],"problem":[25,143],"usually":[27,61],"leads":[28],"to":[29,74,84,103],"spurious":[30,39],"solutions":[31],"in":[32,69,124],"representation":[34],"inertia-gravity":[36,91],"waves.":[37],"The":[38,59,77,111],"modes":[40,60],"have":[41],"wide":[43],"range":[44],"characteristics":[46],"may":[48],"take":[49],"form":[51],"pressure":[53],"(surface-elevation),":[54],"velocity,":[55],"and/or":[56],"Coriolis":[57],"modes.":[58],"cause":[62],"aliasing":[63],"an":[65],"accumulation":[66],"energy":[68],"smallest-resolvable":[71],"scale,":[72],"leading":[73],"noisy":[75],"solutions.":[76],"triangular":[78],"finite-element":[79,149],"pair":[80,150],"$P^{NC}_{1}-P^{}_{1}$":[81],"shown":[83],"\"properly\"":[85],"model":[86],"dispersion":[88,118],"waves,":[92],"this":[94],"achieved":[96],"at":[97,131],"reasonable":[99],"computational":[100],"cost":[101],"compared":[102,153],"traditional":[104],"finite-difference":[105],"schemes.":[106],"Two":[107],"tests":[108],"are":[109,144,152],"proposed.":[110],"first":[112],"test":[113],"examines":[114],"propagation":[116],"fast":[120],"surface":[121],"gravity":[122],"waves":[123],"circular":[126],"basin":[127],"their":[129],"reflection":[130],"lateral":[133],"boundary.":[134],"In":[135],"second":[137],"test,":[138],"results":[139],"Stommel":[142],"presented":[145],"using":[146],"proposed":[148,169],"with":[154,157],"those":[155],"obtained":[156],"C-":[159],"CD-finite-difference":[161],"grids.":[162],"They":[163],"illustrate":[164],"promise":[166],"approach.":[170]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
