{"id":"https://openalex.org/W2069726223","doi":"https://doi.org/10.1137/080737009","title":"A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations","display_name":"A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2069726223","doi":"https://doi.org/10.1137/080737009","mag":"2069726223"},"language":"en","primary_location":{"id":"doi:10.1137/080737009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080737009","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039552338","display_name":"Michael Neilan","orcid":"https://orcid.org/0000-0002-1564-1041"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Neilan","raw_affiliation_strings":["neilan@math.lsu.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"neilan@math.lsu.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011365911"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7968,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.7019764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"47","issue":"4","first_page":"2952","last_page":"2981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9911999702453613,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7781788110733032},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6754423379898071},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6569778919219971},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5548499822616577},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.476191908121109},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.44596919417381287},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.44504427909851074},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12229418754577637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09966170787811279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7781788110733032},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6754423379898071},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6569778919219971},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5548499822616577},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.476191908121109},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.44596919417381287},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.44504427909851074},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12229418754577637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09966170787811279},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080737009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080737009","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.8711","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.8711","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0810.1479v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1518158052","https://openalex.org/W1523631876","https://openalex.org/W1559997346","https://openalex.org/W1684994732","https://openalex.org/W1866311589","https://openalex.org/W1980835848","https://openalex.org/W1989136682","https://openalex.org/W2009863089","https://openalex.org/W2015068148","https://openalex.org/W2028230944","https://openalex.org/W2032316144","https://openalex.org/W2036759661","https://openalex.org/W2041523977","https://openalex.org/W2054715051","https://openalex.org/W2055752660","https://openalex.org/W2061449874","https://openalex.org/W2116442609","https://openalex.org/W2132883347","https://openalex.org/W2140721250","https://openalex.org/W2145754040","https://openalex.org/W2162323386","https://openalex.org/W2177195156","https://openalex.org/W2313087217","https://openalex.org/W3021722416","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4254088695","https://openalex.org/W2367880982","https://openalex.org/W1996772794","https://openalex.org/W2502579552","https://openalex.org/W2360811052","https://openalex.org/W1964128728","https://openalex.org/W2077845843","https://openalex.org/W2112506890","https://openalex.org/W206336013","https://openalex.org/W128188719"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"a":[3,12,23,68,77,105,114],"fully":[4,18,100,115,178],"discrete":[5,116,179],"modified":[6,117,180],"characteristic":[7,118,181],"finite":[8,119,182],"element":[9,120,183],"method":[10,121,137],"for":[11,36,122],"coupled":[13],"system":[14,27],"consisting":[15],"of":[16,72,107,144,175],"the":[17,29,33,54,58,65,73,82,99,123,134,148,156,167,173,176],"nonlinear":[19,101],"Monge\u2013Amp\u00e8re":[20,102],"equation":[21,103],"and":[22,86,170],"transport":[24],"equation.":[25],"The":[26],"is":[28,127],"Eulerian":[30],"formulation":[31],"in":[32,47],"dual":[34],"space":[35],"B.":[37],"J.":[38,89],"Hoskins'":[39],"semigeostrophic":[40,74],"flow":[41,75],"equations,":[42,76],"which":[43,96],"are":[44,162],"widely":[45],"used":[46],"meteorology":[48],"to":[49,165,171],"model":[50],"frontogenesis.":[51],"To":[52],"overcome":[53],"difficulty":[55],"caused":[56],"by":[57,81,104],"strong":[59],"nonlinearity,":[60],"we":[61],"first":[62],"formulate":[63],"(at":[64],"differential":[66],"level)":[67],"vanishing":[69],"moment":[70],"approximation":[71],"methodology":[78],"recently":[79],"proposed":[80,135,177],"authors":[83],"[X.":[84],"Feng":[85],"M.":[87],"Neilan,":[88],"Sci.":[90],"Comput.,":[91],"38":[92],"(2009),":[93],"pp.":[94],"74\u201398],":[95],"involves":[97],"approximating":[98],"family":[106],"fourth-order":[108],"quasilinear":[109],"equations.":[110],"We":[111],"then":[112],"construct":[113],"regularized":[124],"problem.":[125],"It":[126],"shown":[128],"that":[129],"under":[130],"certain":[131],"mesh":[132],"constraint,":[133],"numerical":[136],"converges":[138],"with":[139],"an":[140],"optimal":[141],"order":[142],"rate":[143],"convergence.":[145],"In":[146],"particular,":[147],"obtained":[149],"error":[150],"bounds":[151],"show":[152],"explicit":[153],"dependence":[154],"on":[155],"regularization":[157],"parameter":[158],"$\\varepsilon$.":[159],"Numerical":[160],"tests":[161],"also":[163],"presented":[164],"validate":[166],"theoretical":[168],"results":[169],"gauge":[172],"efficiency":[174],"method.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}