一阶双曲问题的间断流线扩散法

1．引言众所周知，求解一阶双曲问题的Galerkin有限元法，仅具有次最优LZ一收敛阶估计，难于建立H＼误差估计【‘1，且Gderkill有限元解常呈现伪数值振荡．为改善计算精度与稳定性，诸多非标准有限元解法相继提出，其中，间断（Discontinuous）Galerkin有限元法（以下简称DG方法）与流线扩散（StreamlineDiffusion）有限元法（以下简称SD法）是两种具有鲜明特点，较为成功的算法．具体地，DG方法是一种迎风型显式算法，它从入流边界开始，沿流场方向，自上游往下游，逐个单元进行解算，计算十分简便且可局部并行化．SD方法则是一种P…     

强对称的自正交对角拉丁方

1 引言 一个ｎ阶拉丁方是含ｎ个相异元素的集合Ｎ上的一个ｎ阶方阵，其每一行和每一列都是Ｎ的一个置换．ｎ阶拉丁方的一条截态是位于不同行不同列的ｎ个位置使得其中的ｎ个元素两两相异．ｎ阶对角拉丁方是一个ｎ阶拉丁方，其主对角线（位置（）与反对角线（位置（）均为截态． 两个ｎ阶拉丁方Ａ和Ｂ称为正交的（简记作Ａ上Ｂ），如果把它们迭合在一起时，拉丁方Ａ的每一个记号与拉丁方Ｂ的每一个记号相遇一次且仅相遇一次．如果一个ｎ阶拉丁方Ｌ和它自己的转置正交，则称Ｌ为一个自正交的拉丁方，简记为ＳＯＬＳ（ｎ）． ｎ阶自正交对角拉…     

实数域上从正交群到一般线性群的同态

设ｎ，ｍ是自然数且ｎ≥ｍ，本文确定了实数域上从ｎ阶正交群到ｍ阶一般线性群的同态形式．     

零阶贝塞尔函数组成的两个正交系

给出了在常见的函数内积下任意两个零阶贝塞尔函数的内积公式，进而证明了由第一类和第二类零阶贝塞尔函数的线性函数族的正交性以及长度的表达式．     

双曲积分微分方程的有限元方法及其插值后处理技术应用

本文对一类半线性双曲积分微分方程首次应用有限元方法，研究了它的半离散和全离散有限元格式，获得了Ｌ∞（Ｌ２）模意义下的最优误差估计．又对线性双曲积分微分方程利用插值后处理技术获得了Ｌ∞（Ｌ１）模意义下整体超收敛１阶的高精度，而且计算量并未因此增加．本文方法可运用到各类发展型微分及积分微分方程上面．     

高维拟线性双曲型方程组的对角化问题

本文讨论了高维一阶拟线性方程组可对角化的条件，并给出其在二维等熵流方程组、三维空气动力学方程组及具有旋转对称性的守恒律组等情形的应用；然后给出了高维拟线性对角型方程组Ｃａｕｃｈｙ问题存在整体经典解的一个充要条件，并给出其应用。     

自正交拉丁方存在性的一个简短证明

本文是欧拉猜想的一个简明反证.文中给出了所有n≠2,3,6阶的一族自正交拉丁方. §1.引言 1959年和1960年,Bose,Shrikhande和Parker反证了欧拉关于不存在4t+2阶正交拉丁方的猜想,解决了正交拉丁方的存在性问题.1973年Brayton,Coppersmith     

具耗散项拟线性双曲型方程组的边值问题

本文考虑具耗散项一阶拟线性双曲型方程组的具有自由边界的典型自由边值问题．在一些合理假设下,证明了其经典解的整体存在性定理．     

构造正交表的分层方法

利用投影矩阵的正交分解提出了构造正交表的分层方法,作为这种方法的应用构造了一个含有9水平的36阶正交表。     

一类三维拟线性双曲型方程交替方向有限元法

对一类一般的三维拟线性双曲型方程通过转化二阶时间导数得到关于一阶时间导数的耦合方程组,然后进行离散得到交替方向有限元格式,应用微分方程先验估计的理论和技巧得到了最优阶H~1-模和L~2-模误差估计,并给出了数值算例,数值结果和理论分析得到很好的吻合.     

Superconvergence of immersed finite element methods for interface problems

In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of generalized orthogonal polynomials that satisfy both orthogonality and interface jump conditions.     

Superconvergence of finite element approximations to Maxwell's equations

We study superconvergence of edge finite element approximations to the magnetostatic problem and to the time-dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid in R ³, but the grid may be nonuniform. © 1994 John Wiley & Sons, Inc.     

有限元分层快速高精度算法

1.引言 多重网格法和区域分解法实质是有限元空间的分解,在子空间上实行逐次校正迭代或并行校正迭代。[1]对一维有限元空间,利用正交化过程,消去单元内结点,修改单元角点的基函数,提出了所谓快速高精度算法。实例表明,这一算法十分有效。本文对一般区域Ω R~d(d=1,2,3)上有限元空间进行分层正交分解,提出所谓分层快速高精度算法。     

On some relations between spinor and orthogonal groups

In this article we consider Clifford algebras over the field of real numbers of finite dimension. We define the operation of Hermitian conjugation for the elements of Clifford algebra. This operation allows us to define the structure of Euclidian space on the Clifford algebra. We consider pseudo-orthogonal group and its subgroups — special pseudo-orthogonal, orthochronous, orthochorous and special orthochronous groups. As we know, spinor groups are double covers of these orthogonal groups.We proved theorem that relates the norm of element of spinor group to the minor of matrix of the corresponding orthogonal group.     

Superconvergence and asymptotic expansions for linear finite element approximations on crisscross mesh

In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the approximate derivatives.     

Superconvergence and asymptotic expansions for linear finite element approximations on criss-cross mesh

In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the approximate derivatives.     

杂交元零能模式抑制的正交基本变形模式方法

通过杂交元位移场直接推导了单元基本变形模式,并且采用联合正交条件提出一种新的正交化方法,所得到的正交基本变形模式不仅具有简单的变形特征而且和材料参数无关,可以方便有效地考察单元性能,为评价不同杂交元提供了一个统一的参考标准．在此基础上利用柔度矩阵正定性给出一种简单有效的零能模式识别方法,并进一步利用基本变形模式和初始应力模式之间耦合关系,提出一种抑制杂交元零能模式的假设应力场方法,同时指出基本变形模式正交性是抑制单元零能模式的充分必要条件．2D-4节点和3D-8节点单元的数值算例说明了该文基本变形模式方法的有效性．     

An adaptive wavelet viscosity method for hyperbolic conservation laws

We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre‐orthogonal spline‐)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least‐squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Exchange rings,units and idempotents

An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring which contains no infinite set of orthogonal idempotents is an exchange ring if and only if every element is a sum of a unit and an idempo-tent     

An analysis of finite element locking in a parameter dependent model problem

Summary. We consider the bilinear finite element approximation of smooth solutions to a simple parameter dependent elliptic model problem, the problem of highly anisotropic heat conduction. We show that under favorable circumstances that depend on both the finite element mesh and on the type of boundary conditions, the effect of parametric locking of the standard FEM can be reduced by a simple variational crime. In our analysis we split the error in two orthogonal components, the approximation error and the consistency error, and obtain different bounds for these separate components. Also some numerical results are shown. Received September 6, 1999 / Revised version received March 28, 2000 / Published online April 5, 2001