简介:Anecessaryandsufficientconditionofregularityof(0,1,…,m-2,m)interpo-lationonthezerosoftheLaguerrepolynomialsLn(α)(x)(α≥-1)inamanageableformisestablished.Meanwhile,theexplicitrepresentationofthefundamentalpolynomials,whentheyexist,isgiven.Moreover,itisshownthat,iftheproblemof(0,1,…,m-2,TO)interpolationhasaninfinityofsolutions,thenthegeneralformofthesolutionsisf0(x)+Cf1(x)withanarbitraryconstantC.
简介:InthispaperwegiveaconvergencetheoremfornonC^0nonconformingfiniteelementtosolvetheellipticfourthordersingularperturbationproblem.Twosuchkindofelements,anineparametertriangularelementandatwelveparameterrectangularelementbothwithdoublesetparameters,arepresented.Theconvergenceandnumericalresultsofthetwoelementsaregiven.
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简介:Inthisarticleweconsideratwo-levelfiniteelementGalerkinmethodusingmixedfiniteelementsforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThemethodyieldsaH^1-optimalvelocityapproximationandaL^2-optimalpressureapproximation.Thetwo-levelfiniteelementGalerkinmethodinvolvessolvingonesmall,nonlinearNavier-StokesproblemonthecoarsemeshwithmeshsizeH,onelinearStokesproblemonthefinemeshwithmeshsizeh<