资源描述：
《A New Family of Mixed Finite Elements in R3 Nedelec 1986》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。
1、NumerischeNumer.Math.50,57-81(1986)Mathematik9Springer-Verlag1986ANewFamilyofMixedFiniteElementsin]R3J.C.N6d~lecMath~matiqucsApplique6cs,EcolePolytechniquc,F-91120Plaiseau,FranceSummary.Weintroducetwofamiliesofmixedfiniteelementonconfor-minginH(div)andoneconform
2、inginH(curl).ThesefiniteelementscanbeusedtoapproximatetheStokes'system.SubjectClassifications:AMS(MOS):65N30;CR:G1.8.1.IntroductionThemixedfiniteelementwasintroducedfirstinseveralpapersofFraeijsDeVeubeke.In1977,RaviartandThomas[8]usedtheseelementsforsolvingsecond
3、orderequationsintwodimension.In1980[6],weintroducedtwofamiliesofmixedfiniteelementsinthreedimension.ThefirstfamilygeneralizesthatofP.A.Raviart-J.M.ThomasandisconforminginthespaceH(div).ThesecondoneappearstobecompletelynewandisconforminginthespaceH(curl).In1982,in
4、thereference[7],weusedthenewfiniteelementstointroduceanapproximationoftheStokesequationsthatgeneralizestothe3Dcase,the(~,co)approximation.in1984,Brezzietal.[2]introducedanewmixedfiniteelementconforminginH(div)intwodimensions.Thislastpaperisthestartingpointofonsea
5、rchfornewfamiliesofmixedfiniteelementsinthreedimension.Weintroduceheretwofamiliesofsuchfiniteelements.ThefirstoneisconforminginthespaceH(div)andinfactthisfamilyissplitinthreecorrespondingtothecaseoftetrahedrons,cubesandprisms.Thesecondfamilyisconforminginthespace
6、H(curl)andisalsosplitintothreeparts.Wedescribetheseelements,provetheunisolvenceandestimatetheinterpolationerror.Whenwritingthispaper,welearnedthatBrezzi,Douglas,DuranandFortinobtainedsimilarresultsforsomefiniteelementsinH(div).Theyobtainedresultsforthecaseoftetra
7、hedraandcubes.Apparentlytheirdegreesoffreedomaredifferentfromours.Inthelastchapter,wedescribethewayourelementscanbeusedtoapproximatetheStokes'system.58J.C.Nhd61ecNotationsKisatetrahedron,acubeoraprism,itsvolumeisSdx;K0Kisitsboundary;nisthenormaltothisboundary;fis
8、afaceofK,withareaSdT;faisanedgeofKwithlength~ds;aLZ(K)isthespaceofsquareintegrablefunctionsdefinedonK;Hm(K)={~beL2(K),8~b~L2(K);]a]
