一种基于WENO重构的半离散中心迎风格式

通过三阶WENO重构和半离散中心迎风数值通量的结合,给出了一种求解双曲型守恒律方程的三阶半离散中心迎风格式,格式保持了中心差分格式方法简单的优点．数值计算的结果表明该方法具有较高的分辨率．     

一类混合MUSCL型E格式收敛性的研究

０．引 言 我们知道ＴＶＤ格式能高效地捕捉激波,特别是在激波附近解不发生振荡,因此在流体力学数值计算中得到了广泛的应用．但在 １９８５年,Ｊ．Ｇｏｏｄｍａｎ和 Ｒ．Ｌｅｖｅｑｕｅ证明了二维守恒型 ＴＶＤ格式至多是一阶精度格式［６］,而 ＭｍＢ格式［１］的提出使构造二维高精度格式有了新的突破．另外,在传统理论下,差分格式的熵条件是很难证明的．文［２］提出了在多维空间变量下的高精度差分格式下收敛性的一般方法．证明中只须假设格式解的一致ｌ∞估计和空间离散熵的弱估计,然后运用 Ｄｉｐｅｒｎａ的唯一性定理［５］…     

一个实用的本性并行差分格式

１．引 言 近些年来随着计算机尺度和复杂性的扩大，人们对计算机和计算方法提出了更高的要求．这表明了人们不仅需要高速的，大内存的并行计算机，而且需要有效的并行算法．为了适合并行计算。一些数值格式需要重新改造．然而确有一些数值格式本身具有并行特征，能够直接用于并行计算． 事实上，关于偏微分方程的有限差分格式都有这种情况，现在人们正尽力研究它们，并给出了一些方法［１，２］．在这篇文章里，我们以如下问题为例：给出了一个实用的本性并行差分格式．此格式基于在子区域边界上用显式格式，内部用隐式格式，此格式有许多…     

基于元数据和XML的信息抽取与集成技术研究

为了得到统一的数据形式以利于数据操作和处理,提出了采用基于元数据的模板定制技术以实现信息抽取的方法．该方法有效地实现对非结构化文本的信息提取,将抽取信息转换为统一的XML格式,然后将XML格式的信息集成到关系数据库中．本方法在某造船厂的企业信息化中得到成功应用,为解决企业的信息集成问题提供了一种面向Word文档的新方案．     

用JDOM和XML实现异构数据库的数据提取

大量分散的形式及不同格式的数据给现代数据处理带来了越来越大的困难。为统一数据形式以利于数据操作和处理，讨论了将形式多样的数据格式转换成统一的XML（Extemible Markupbnguage）格式的问题。对数据源中不同格式文件数据．按照预先定义的XML模板，以格式说明文件结构统一描述．并提取数据或作进一步的处理．最后转换为XML格式输出。文中论述了从数据库中提取数据转换为XML格式的方法及步骤，并且方法简单实用．可以推广到对所有格式数据的提取。     

迎风紧致格式与热流计算

１．引 言 众所周知,ＴＶＤ格式是能够高质量地捕捉激波的方法,但在计算粘性绕流时许多ＴＶＤ格式数值耗散太大,不能正确模拟粘性流动,因而无法正确计算热流值．文献［３］指出,采用高精度格式可适当放松对网格雷诺数的要求,因此发展三阶或三阶以上的格式是需要的．文献［４］研究了迎风紧致群速度控制格式（ＵＣＧＶＣ格式）在 Ｅｕｌｅｒ方程中的应用,提高了对激波的分辨率,优于通常二阶精度ＴＶＤ格式．本文在文献［４］的基础上给出了利用迎风紧致格式求解ＮＳ方程．它是ＵＣＧＶＣ格式在粘性流计算中的推广．对于方程中的无粘…     

一种简化的三阶精度加权ENO格式

91．引言从七十年代后期开始，对双曲型守恒律方程数值方法的研究以VanLeer构造出来的MUSCL格式［‘］为先导，出现了一些全新的高分辨率守恒型差分格式．特别是A．Harten［‘］提出了TVD（TotalVariationDiminising）格式的概念后，双曲型守恒律方程数值方法的研究取得了飞速的发展．因为TVD格式可以保持数值解的单调性，所以它可以有效地抑制间断附近数值解的振荡，这方面有重要代表性的工作是［2－4］．由于TVD格式必须保证数值解的总变差不增，所以使得TVD格式在光滑解的局部极值点处降价．为了克服TVD格式的这个弱点，便出…     

基于规则图形的连接关系生成算法及其开放格式表达

以一种开放的格式来表迭规则图形厦其连接关系将极大地提高囤、数一体化数据共享能力，降低重复开发现象．文章分析了规则图形连接关系的形成特点，利用囤论的思想形式化地描述了规则图形的形成过程度其连接关系矩阵的生成算法，并给出了基于SVG格式的图、数一体化的开放格式表迭方法．     

借助HTML语言实现格式数据打印

介绍了一种使用Visual C＋＋．NET新特性借助HTML语言进行格式数据打印的实现方法。这种方法以HTML文件为基础,通过．NET中MFC的CDHtmlDialog类对其进行封装,巧用类CDHtmlDialog的对话框资源作为子窗口,直接以打印相关操作按钮的方式,随意嵌入需要完成打印功能界面窗口的位置,实现了格式数据打印。     

Microsoft Systems Management Server（SMS）OS Deployment Feature Pack使用的Windows Image（WIM）格式是Windows Vista要使用的最终版本吗？

不是的。SMS OS Deployment Feature Pack使用的WIM格式可以认为是WIM格式的0．9版,这种格式的1.0版随着Vista一起发布。SMS 4．0（现在称之为SCCM2007）完全支持Vista WIM（1．0）格式,     

A Galerkin finite element scheme for time–space fractional diffusion equation

In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method.     

Decentrage et elements finis mixtes pour les equations de diffusion-convection

We analyze a numerical scheme for scalar diffusion-convection equations. The convective term is approximated by an upwind scheme for discontinuous finite elements and the diffusion term is approximated by a mixed finite element method. Studying large convection problems, we calculate estimates which remain valid when the diffusion term vanishes. Since the error analysis shows that the convection term is approximated less precisely than the diffusion term, the initial formulation is modified in order to balance errors from these two terms.      

An assessment of discretizations for convection-dominated convection–diffusion equations

The performance of several numerical schemes for discretizing convection-dominated convection–diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov–Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.     

Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations

In this paper, a class of distributed-order time fractional diffusion equations (DOFDEs) on bounded domains is considered. By L1 method in temporal direction, a semi-discrete variational formulation of DOFDEs is obtained firstly. The stability and convergence of this semi-discrete scheme are discussed, and the corresponding fully discrete finite element scheme is investigated. To improve the convergence rate in time, the weighted and shifted Grünwald difference method is used. By this method, another finite element scheme for DOFDEs is obtained, and the corresponding stability and convergence are considered. And then, as a supplement, a higher order finite difference scheme of the Caputo fractional derivative is developed. By this scheme, an approach is suggested to improve the time convergence rate of our methods. Finally, some numerical examples are given for verification of our theoretical analysis.     

Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems

In this paper, we study the stability and accuracy of adaptive finite element methods for the convection-dominated convection-diffusion-reaction problem in the two-dimension space. Through various numerical examples on a type of layer-adapted grids (Shishkin grids), we show that the mesh adaptivity driven by accuracy alone cannot stabilize the scheme in all cases. Furthermore the numerical approximation is sensitive to the symmetry of the grid in the region where the solution is smooth. On the basis of these two observations, we develop a multilevel-homotopic-adaptive finite element method (MHAFEM) by combining streamline diffusion finite element method, anisotropic mesh adaptation, and the homotopy of the diffusion coefficient. We use numerical experiments to demonstrate that MHAFEM can efficiently capture boundary or interior layers and produce accurate solutions.     

Stabilized discontinuous Galerkin method for hyperbolic equations

In this work a new stabilization technique is proposed and studied for the discontinuous Galerkin method applied to hyperbolic equations. In order to avoid the use of slope limiters, a streamline diffusion-like term is added to control oscillations for arbitrary element orders. Thus, the scheme combines ideas from both the Runge-Kutta discontinuous Galerkin method [J. Scient. Comput. 16 (2001) 173] and the streamline diffusion method [Comput. Methods Appl. Mech. Engrg. 32 (1982)]. To increase the stability range of the method, the diffusion term is treated implicitly. The result is a scheme with higher order in space with the same stability range as the finite volume method. An optimal relation between the time step and the size of the diffusion coefficient is analyzed for numerical precision. The scheme is implemented using the object oriented programming philosophy based on the environment described in [Comput. Methods Appl. Mech. Engrg. 150 (1997)]. Accuracy and shock capturing abilities of the method are analyzed in terms of two bidimensional model problems: the rotating cone and the backward facing step problem for the Euler equations of gas dynamics.     

A discontinuous finite difference streamline diffusion method for time-dependent hyperbolic problems

In this article, a new finite element method, discontinuous finite difference streamline diffusion method (DFDSD), is constructed and studied for first-order linear hyperbolic problems. This method combines the benefit of the discontinuous Galerkin method and the streamline diffusion finite element method. Two fully discrete DFDSD schemes (Euler DFDSD and Crank–Nicolson (CN) DFDSD) are constructed by making use of the difference discrete method for time variables and the discontinuous streamline diffusion method for space variables. The stability and optimal L² norm error estimates are established for the constructed schemes. This method makes contributions to the discontinuous methods. Finally, a numerical example is provided to show the benefit of high efficiency and simple implementation of the schemes.     

A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations

We propose a discontinuous Galerkin finite element method for convection diffusion equations that involves a new methodology handling the diffusion term. Test function derivative numerical flux term is introduced in the scheme formulation to balance the solution derivative numerical flux term. The scheme has a nonsymmetric structure. For general nonlinear diffusion equations, nonlinear stability of the numerical solution is obtained. Optimal kth order error estimate under energy norm is proved for linear diffusion problems with piecewise P ^k polynomial approximations. Numerical examples under one-dimensional and two-dimensional settings are carried out. Optimal (k+1)th order of accuracy with P ^k polynomial approximations is obtained on uniform and nonuniform meshes. Compared to the Baumann-Oden method and the NIPG method, the optimal convergence is recovered for even order P ^k polynomial approximations.     

An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions

In this paper, a novel energy-preserving numerical scheme for nonlinear Hamiltonian wave equations with Neumann boundary conditions is proposed and analyzed based on the blend of spatial discretization by finite element method (FEM) and time discretization by Average Vector Field (AVF) approach. We first use the finite element discretization in space, which leads to a system of Hamiltonian ODEs whose Hamiltonian can be thought of as the semi-discrete energy of the original continuous system. The stability of the semi-discrete finite element scheme is analyzed. We then apply the AVF approach to the Hamiltonian ODEs to yield a new and efficient fully discrete scheme, which can preserve exactly (machine precision) the semi-discrete energy. The blend of FEM and AVF approach derives a new and efficient numerical scheme for nonlinear Hamiltonian wave equations. The numerical results on a single-soliton problem and a sine-Gordon equation are presented to demonstrate the remarkable energy-preserving property of the proposed numerical scheme.     

Adaptive finite element heterogeneous multiscale method for homogenization problems

In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfinite elements. The desired macroscopic solution is obtained by a suitable averaging procedure based on microscopic data. As the macroscopic data (such as the macroscopic diffusion tensor) are not available beforehand, appropriate error indicators have to be defined for designing adaptive methods. We show that such indicators based only on the available macro- and microsolutions (used to compute the actual macrosolution) can be defined, allowing for a macroscopic mesh refinement strategy which is both reliable and efficient. The corresponding a posteriori estimates for the upper and lower bound are derived in the energy norm. In the case of a uniformly oscillating tensor, we recover the standard residual-based a posteriori error estimate for the finite element method applied to the homogenized problem. Numerical experiments confirm the efficiency and reliability of the adaptive multiscale method.