HIGH ACCURACY ANALYSIS FOR FIRST ORDER HYPERBOLIC EQUATIONS BY PETROV-GALERKIN METHODS

1.IntroductionInthispaper,weareconcernedwiththefiniteelementmethodforthefollowingfirstorderhyperbolicequationwithsomeinitial--boundaryconditionwheref,gandvaresufficientlysmoothgivenfunctions.ItiswellknownthatthestandardGalerkinfiniteelementmethodisnotasvalidtothefirstorderhyperbolicproblemsasitistotheellipticandtheparabolicproblems.TheaccuracyofGalerkinll]solutionsfortheabetorderhyperbolicproblems,roughlyspeaking,losesoneorderwithrespecttotheaccuracyofthefiniteelemelltspaces.Moreover,Galerki…     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

CORRECTION FOR COLLOCATION SOLUTIONS OF WIENER－HOPF EQUATIONS

ＣＯＲＲＥＣＴＩＯＮＦＯＲＣＯＬＬＯＣＡＴＩＯＮＳＯＬＵＴＩＯＮＳＯＦＷＩＥＮＥＲ－ＨＯＰＦＥＱＵＡＴＩＯＮＳ￥ＳＨＩＪｕｎ；ＬＩＮＱｕｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，...     

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

FINITE ELEMENT ERROR EXPANSIONS FOR THE EIGENVALUE APPROXIMATION TO THE MULTIGROUP DIFFUSION EQUATIONS

Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R~n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for nonuniform quadrilateral meshes,and finally for nonuniformhexahedral meshes.The effect of certain classes of numerical integrations is studied.As applicationsof the expansions,several extrapolation formulas and a posteriori error estimates are obtained.     

MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1. IntroductionWe consider a Volterra integro-differential equationwith initial condition u(0) = not where f, P, k are continuous on their respective domainsJ, JxR and axs (n:~ {(t,s): 05s5t5T}) such that (1.l) possesses a unique solutionu E C'(J).It has been shown in [1] that the collocation approximation for (1.1) by discolltinuous piece--wise polynomial spline collocation at the Gauss points restore optimal local superconvergenceat the knots but does not yield global superconvergence on…     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

GLOBAL SUPERCONVERGENCE ANALYSIS OF WILSON ELEMENT FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.     

NON-CLASSICAL GENERALIZED SOLUTIONS FOR SOME HYPERBOLIC SYSTEMS

1.IntroductionThemostspecialfeatureofconservationlawsofhyperbolicsystemsisthattheirsolutionsalwayshavediscolltinuities.ThiskindofdiscontinuityrepresentstheshoCkwavephenomena.Sopeopleintroducetheideaofgeneralizedsolutionwhichsatisfiesequationsinthesenseofdistribution.Underthisdefinition,alotofachievementshavebeenobtainedsince1950'sinthisfield.However,inrecelltyears,manyauthors(see[l--6])discoveredthatthereisnoexistenceanduniqllenessofsolutionstoRiemannproblemsforsomeconservationlaws.Bynumeric…     

A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

In this paper,the linear mixed finite element method is considered forthe biharmonic Dirichlet boundary value problem.Almost optimal error estimates,superconvergence estimates and the derivative error expansion are obtained.     

NONHOMOGENEOUS HOPF EQUATIONS IN HIGHER DIMENSIONS

1.IntroductionWeconsiderthefollowingequationsHeretheunkownfunctionisu~(ul,u2)'',u.)andu'V~Z:=,nib.Whenn~1,(1.1)isBurger'sequationwithviscosityeand(1.2)isHopfequationwithnonhomogeneoustermb(x,t).Ladyzhenskayahajsinvestigatedtheinitial-boundaryvalueproblom…     

A PRIORI L~2 ERROR ESTIMATES FOR GALERKIN METHODS FOR NONLINEAR SOBOLEV EQUATIONS

In this paper we study Galerkin approximations to the solution of the nonlinearSobolev equation c(u)u_t=▽·{a(u)▽u_t+b(u)▽u}+f(u)in two spatial dimensions and deriveoptimal L~2 error estimates for the continuous-time,Crank-Nicolson and extrapolated Crank-Nicolson discrete-time approximations.     

THE EXTRAPOLATION METHOD FOR A CLASS OF NON-SMOOTH FREDHOLM INTEGRAL EQUATIONS

For a class of non-smooth Fredholm integral equations we prove thatRichardson extrapolation method can be used to increase accuracy for finite ele-ment methods.On the basis of local refinement mesh,a superconvergence result isshown.Our theory also covers a class of non-smooth Wiener-Hopf equations andan application includes the calculation in certain linear elastic fracture problems.     

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

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BLOW-UP SOLUTIONS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

The type of problem under consideration is where D is a smooth bounded domain of RN, q = |(?)u|2. By constructing an auxiliary function and using Hopf's maximum principles on it, existence theorems of blow-up solutions, upper bound of "blow-up time" and upper estimates of "blow-up rate" are given under suitable assumptions on a, b, f, g, σand initial date U0(X). The obtained results are applied to some examples in which a, b, f, g and σare power functions or exponential functions.     

EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

In this paper,a numerical analysis of finite element methods for Fredholm equationsof the first kind,which is based upon regularization,is made.It shows that extrapolationalgorithms can accelerate the convergence of approximate solutions.     

SOME STABILITY THEOREMS FOR DIFFERENCE EQUATIONS WITH TIME DELAY

1.IntroductionDifferellceequationswithtimedelayhavebeenanimportantclassofmathematicallllodels.Fol'instance,inbiology,systemsofdifferenceequationshavebeedmuchusedtomodeltheinteractiollsofspecieswithlion-overlappinggeneration,butthemodelwillberelatedtodifferenceequationswithtimedelaywhenollemustconsidertheinfluenceoftimedelayeffectforspecies11limber.Thereisextensiveresearchondifferentialequationswithtimedelaybutthereisoillylittleworkdoneondifferenceequationswithtimedelay.Ouraimistoestablishstabi…     

QUENCHING PHENOMENA FOR SYSTEMS OF SEMILINEAR PARABOLIC EQUATIONS I

1.IntroductionConsiderthefollowinginitial-boundaryvalueproblemforthesystemsofsemilinearparabolicequationsWhereG.~(--a,a)x(0,Ta),r.~({--a,a}x[0,Ta))U([--a,a]x{0}),andf(z)andg(z)satisfy(FGI)f(z):(--co,ba)-R ,g(z):(--co,bl)-R ,f(0)>0,andg(0)>0;(FG2)i(z)andg(…     

成败型产品环境因子的经典近似限

利用Poisson近似和正态近似,本文导出了二项分布,负二项分布以及二项～负二项分布环境因子的经典近似限。     

ON A PROPERTY OF SOLUTIONS OF M-MATRIXEQUATIONS

1.IntroductionConsideringthefollowingsystemoflinearequationsAx~b(l.1)whereAisannxnM-matrix,bisanndimensionalvectorandbeRang(A).Theresearchonthesolutionofequation(1.1)isveryimportantinLeontiefmodelofinput-outputanalysis(see[1,2]).G.St..k.ma[Zjstudiestheabo…