P1-NONCONFORMING QUADRILATERAL FINITE VOLUME ELEMENT METHOD AND ITS CASCADIC MULTIGRID ALGORITHM FOR ELLIPTIC PROBLEMS

In this paper,we discuss the finite volume element method of P_1-nonconforming quadri-lateral element for elliptic problems and obtain optimal error estimates for general quadri-lateral partition.An optimal eascadie multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization.Numerical experimentsare reported to support our theoretical results.     

A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SPACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM

1.IntroductionQuasi-Newtonmethodsplayanimportantroleinnumericallysolvingnon--linearsystemsofequationsontheEuclideanspaces.Blltitseemsthatthequasi-Newtonmethodshavenotbeenapplieddirectlytosolvinginverseproblemsinpartialdifferentialequations(PDE)uptonowifwe…     

马氏双链函数的强大数定律及其应用

本文研究了马氏随机环境中马氏双链函数的强大数定律.利用将双链函数进行分段研究的方法,获得了马氏环境中马氏双链函数强大数定律成立的一个充分条件.运用该定律,推导出马氏双链从一个状态到另一个状态转移概率的极限性质,进而推广了马氏双链的极限性质.     

多孔介质中两相不可压混溶驱替的差分流线扩散法及其误差分析

多孔介质中两相不可压混熔驱替问题可描述为椭圆和抛物耦合的非线性偏微分方程组，对椭圆方程采用混合元方法，而对抛物方程采用差分流线扩散法，本文构造了求解该问题的差分流线扩散-混合元格式，最后，给出所构造格式按L^∞(L^2）模的拟最优误差阶估计。     

Newton法及其各种变形收敛性的统一判定法则

１引言Ｂａｎａｃｈ空间中的算子方程是非常广泛的应用数学课题,而求方程数值解的主要方法是Ｎｅｗｔｏｎ法及其各种变形．自从Ｋａｎｔｏｒｏｖｉｃｈ关于Ｎｅｗｔｏｎ法收敛性的著名定理建立以来,有大量的文献在种种相仿的条件下研究各种变形收敛性的各种判定法则．在此,本文建立了统一的判定法则．首先,把Ｋａｎｔｏｒｏｖｉｃｈ算子类Ｋ（１）（ｘ０,ｙ）扩充为Ｋ（１）（ｘ０,ｙ,Ｃ）,并给出类Ｋ（１）（ｘ０,ｙ,Ｃ）的扩类Ｋｃｅｎｔ（１）（ｘ０,ｙ,Ｃ）和子类Ｋ（２）（ｘ０,ｙ,Ｃ）．对于这些算子类,确定了一个仅依…     

研究国际证券投资及其有效集的多目标线性规划方法

本文给出国际证券组合投资决策的多目标线性规划模型，以及求解有效国际证券组合的偏好系数加权法．在此基础上，应用线性多数规划技术研究有效国际证券组合集的几何特征，并给出相应结论和简单算例．     

LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.     

GALERKIN METHOD FOR COMPRESSIBLE FLOW OF CONTAMINATION FROM NUCLEAR WASTE WITH MOLECULAR DIFFUSION AND DISPERSION*

Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We'll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L~2 and H~1 is proved. A contribution of this paper is how the dispersion term can be handled,