{"refrec":{"BRefID":211403,"RR":"<b>Comblen, R.; Legrand, S.; Deleersnijder, E.; Legat, V.</b> (2009). A finite element method for solving the shallow water equations on the sphere. <i>Ocean Modelling 28(1-3)</i>: 12-23. <a href=\"http://dx.doi.org/10.1016/j.ocemod.2008.05.004\" target=\"_blank\">dx.doi.org/10.1016/j.ocemod.2008.05.004</a>","BEntID":203325,"PublicFlag":1,"CheckedFlag":1,"wosflag":1,"vabbflag":1,"RefStringPartII":". <i>Ocean Modelling 28(1-3)</i>: 12-23. <a href=\"https://dx.doi.org/10.1016/j.ocemod.2008.05.004\" target=\"_blank\">https://dx.doi.org/10.1016/j.ocemod.2008.05.004</a>","DocTypID":8,"DocType":"Journal article","MarineFlag":0,"FreshFlag":0,"BrackishFlag":0,"TerrestrialFlag":0,"Authorstring":"Comblen, R.; Legrand, S.; Deleersnijder, E.; Legat, V.","OrigTitleTranslFlag":0,"Authorstringtrunc":"Comblen, R. <i>et al.</i>","Englishabstract":"Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. <br>Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the <i>P</i><sub>1</sub><sup>NC</sup> - <i>P</i><sub>1</sub> finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.","AbstractOtherLang":null,"BibLvlCode":"AS","StandardTitle":"A finite element method for solving the shallow water equations on the sphere","OrigTitleLangCode":"en","OrigTitleLangCodeExtended":"eng","OrigTitleLangID":15,"DateLastModified":{"date":"2024-12-10 01:33:01.897972","timezone_type":1,"timezone":"+01:00"},"UserAccessRight":null,"UserAccID":null,"AuthorKeywords":"Curved manifolds; Finite element; Shallow water equations; Spherical","OtherDescriptors":null,"Notes":null,"AnaPub":2009,"MonPub":null,"DateUpdate":"2012-01-27","DateCreate":"2011-12-22","SecASFANote":null,"ConfID":null,"PeerRev":1,"VlizCoreFlag":1,"WoScode":"WOS:000265400800003","VABBcode":null,"OpenAcc":0,"DOI":"10.1016/j.ocemod.2008.05.004"},"refs":null,"anarec":{"AnaID":211403,"PubliDate":2009,"Pagination":"12-23","XtraPublOfAnaID":null,"ISBN":null,"Volume":"28","Issue":"1-3","BRefMon":null,"BRefMonRR":null,"BRefXtra":null,"BRefXtraRR":null,"SerBRefID":45570,"SerRR":"Ocean Modelling. 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ISSN 1463-5003; e-ISSN 1463-5011","StandardTitleSer":"Ocean Modelling","ISSN":"1463-5003","AbbrevSer":"Ocean Modelling","StandardTitleMon":null,"StartPage":12,"Pages":12,"ToPubliDate":null,"BRefBibLvlCode":"S","SerNotes":null},"monrec":null,"serrec":null,"relations":null,"relationsRev":null,"addrec":null,"othpubs":null,"ownerships":null,"authors":[{"AutName":"Comblen","Firstname":"Richard","Initials":"R.","Affiliation":"Univ Catholique Louvain, Ctr Syst Engn & Appl Mech, B-1348 Louvain, Belgium.","Discriminator":null,"CorporateFlag":0,"BEntID":203325,"AutID":140827,"OrderNr":1,"DegrID":null,"EditorFlag":0,"CorrespFlag":0,"IllustratorFlag":0,"ReviserFlag":0,"TranslatorFlag":0,"InsAcronym":"CESAME","InsFSN":"Université Catholique de Louvain; Centre d'ingénierie des systèmes d'automatique et de mécanique appliquée","ORCID":null,"PersID":27304,"InsID":8859},{"AutName":"Legrand","Firstname":"Sébastien","Initials":"S.","Affiliation":"Royal Belgian Inst Nat Sci, Management Unit N Sea Math Models, B-1200 Brussels, Belgium.","Discriminator":null,"CorporateFlag":0,"BEntID":203325,"AutID":140828,"OrderNr":2,"DegrID":null,"EditorFlag":0,"CorrespFlag":0,"IllustratorFlag":0,"ReviserFlag":0,"TranslatorFlag":0,"InsAcronym":"BMM","InsFSN":"Koninklijk Belgisch Instituut voor Natuurwetenschappen; 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