THE ERRORS ESTIMATION OF THE CHEBYSHEV SPECTRAL－DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORTICITY EQUATION

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CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR INCOMPRESSIBLE FLUID FLOW

In this paper, we propose a mixed method for solving two-dimensional unsteady vorticity equations by using Chebyshev spectral-fiuite element approximation. The generalized stability and the optimal rate of convergence are proved. The numerical results show the advantages of such method. The technique in this paper is also useful for other nonlinear problems.     

CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

1. IntroductionSpectral method has been used successfu11y in computational fluid dynamics. FOr semi-periodic problems, we can use mixed FOurier-Chebyshev spectral method, FOurier spectral-finitedifference method and FOurier spectral-finite element method …     

FOURIER-CHEBYSHEV PSEUDOSPECTRAL METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION WITH UNILATERALLY PERIODIC BOUNDARY CONDITION

A Fourier-Chebyshev pseudospectral scheme is proposed for three-dimensionalvorticily equation with unilaterally periodic boundary condition. The generalized stability and convergence are analysed. The numerical results are presented.     

ON LOCKING-FREE FINITE ELEMENT SCHEMES FOR THREE-DIMENSIONAL ELASTICITY

In the present paper,the authors discuss the locking phenomenon of the finite elementmethod for three-dimensional elasticity as the Laméconstant λ→∞.Three kinds of finiteelements are proposed and analyzed to approximate the three-dimensional elasticity withpure displacement boundary condition.Optimal order error estimates which are uniformwith respect to λ∈(0,+∞)are obtained for three schemes.Furthermore,numerical resultsare presented to show that,our schemes are locking-free and and the trilinear conformingfinite element scheme is locking.     

Sobolev方程的连续时空有限元方法

本文研究Sobolev方程的连续时空有限元方法.首先建立Sobolev方程的连续时空有限元格式,然后证明了解的存在唯一性和稳定性并给出连续时空有限元解各种范数下的误差估计.最后给出数值算例来验证理论分析的正确性,并进一步说明本文所建立的格式关于时间可以得到比传统有限元方法更高的精度.     

反应扩散方程的连续时空有限元方法

本文研究了反应扩散方程的连续时空有限元方法.首先建立了其连续时空有限元格式并证明了有限元解的存在唯一性及稳定性.然后通过引入时空投影算子在没有时空网格限制的条件下给出其近似解在节点处的L~2,H~1最优范数估计以及全局L~2(L~2),L~2(H~1)最优范数估计.最后给出两个数值算例来验证方法的有效性与灵活性并说明结论的正确性.     

LEGENDRE SPECTRAL-FINITE ELEMENT METHOD FOR THE THREE-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

This paper is devoted to the mixed Legendre spectral-finite element approximation of the three-dimensional, non-periodic, unsteady Navier-Stokes equations. A class of fully discrete schemes are constructed with artificial compression. The generalized stability and convergence are proved strictly on the assumption that the two-dimensional inf-sup condition of the finite element approximation is satisfied.     

粘弹性方程一种新的分裂正定混合元法

本文用分裂正定混合有限元方法研究二阶粘弹性方程. 首先构造一种新的分裂正定混合变分形式和基于这种分裂正定混合变分形式关于时间的半离散格式, 然后绕开关于空间变量的半离散化格式, 直接从时间半离散出发构造出全离散化的分裂正定混合有限元格式, 并给出这种分裂正定混合有限元解的误差估计. 这种研究思路使得理论论证变得更简单,这是处理二阶粘弹性方程的一种新的尝试.     

波动方程单位分解有限元法及收敛性分析

<正>1引言与问题的提出自黄云清和许进超提出基于单位分解技术的重叠型非匹配网格有限元方法以来,这类方法日益引起人们极大的兴趣.这篇文章将这类有限元方法运用到波动方程当中,分别研究了重叠型非匹配网格波动方程半离散和全离散有限元方法,给出了有限元解及其梯度的误差估计.下面先给出模型问题的简单介绍.     

GLOBAL SUPERCONVERGENCE ESTIMATES OF FINITE ELEMENT METHOD FOR SCHRODINGER EQUATION

1.IntroductionConsiderthefollowinginitialboundaryvalueproblemofSchr6dingerequationwheren~[0,1]',at~On/Ot,T>0isaconstant.Theequivalentvariationalformof(1.1)is:foralltE[0,T],findu(t)6Hi(n)satisfiesthefollowingvariationalequation:where(w,v)~IwvdxdenotestheinnerproductofL'(fl)anda(u,v)~(Vu,Vv),ibetheimaginaryunit.Weassumethatthefunctionsarecomplex--valuedandHibertspacesarecomplexspaces.LetThbeaquasiuniformrectangulationoffiwithmeshsizeh>0andS'(O)CHi(fi)bethecorrespondingpiecewisebilinearpol…     

THE CHEBYSHEV SPECTRAL METHOD WITH A RESTRAINT OPERATOR FOR BURGERS EQUATION

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双调和方程混合元的一种新格式

本文介绍了双调和方程混合元的一种新格式,用双二次多项式逼近流函数,双一次多项式逼近涡函数.在拟一致矩形剖分的条件下,证明了此格式具有与C-R格式中分别用双二次多项式逼近相同的收敛阶.     

非线性双曲型方程的混合元方法

1　引　　言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t),　　x∈Ω,t∈J,(1.1)u(x,0)=u0(x),　　x∈Ω,(1.2)ut(x,0)=u1(x),　　x∈Ω,(1.3)u(x,t)=-g(x,t),　　(x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献   

非线性Schrdinger方程新混合元方法的高精度分析

基于双线性元及其梯度所属空间,建立了非线性Schrdinger方程的自由度少且易满足B-B条件的新混合元格式.首先,利用双线性元的高精度分析和导数转移技巧,在半离散格式下,导出了原始变量在H~1模及流量在L~2模意义下的超逼近性质,进而,借助于插值后处理算子,得到了整体超收敛结果.最后,对向后:Euler和Crank-Nicolson-Galerkin全离散格式分别给出了原始变量的H~1模及L~2模和流量的L~2模误差分析,并通过数值算例,表明逼近格式是高效的.     

A TRIANGULAR FINITE VOLUME ELEMENT METHOD FOR A SEMILINEAR ELLIPTIC EQUATION

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.     

THE CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stability and convergence of this new scheme.     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

1. IntroductionConsider the advection--diffusion equationin a bounded polygonal domain fl c IR2 with the boundary an, where o < K << 1 is thediffusion parameter, rr > 0 is a given positive constant, g(x) is a given vector field representingthe flow with V…     

非线性抛物型方程的变网格有限元法

Three linear finite element schemes with moving mesh are established for a class of nonlinear parabolic equations.Optimal L^2-norm and energy norm error estimates are derived under certain conditions.     

粘性不可压缩对流占优Oseen方程的非协调子格稳定化有限元法分析

<正>1引言本文考虑粘性不可压缩对流占优Oseen方程,(?)(1)其中:Ω(?)R~d(d=2)为具有Lipschitz连续边界的有界开集,β∈W~(1,∞)(Ω)且▽·β=0,μ、σ为常数,f∈L~2(Ω).当采用通常的混合有限元方法(MFEM)求解时,一般会遇到以下两个困难:·为保证速度和压力数值解稳定,要求有限元空间满足inf-sup(or Babuska-Brezzi)条件.·当对流占优,即0μ《||β||_(L~∞(Ω))时,数值解会产生伪振荡.