一类新的分层基以及非线性Galerkin方法

本文首先讨论了一类新的分层基函数，该基函数具有小波和有限元两方面的优点，特别适用于用来构造耗散型发展方程的非线性Ｇａｌｅｒｋｉｎ算法．本文利用该基函数对一类抽象发展方程给出了其非线性Ｇａｌｅｒｋｉｎ算法。并分析了该算法的收敛性，给出了误差估计。     

半离散非线性Galerkin算法的收敛性

本文给出了求解非线性发展方程的半离散非线性Ｇａｌｅｒｋｉｎ算法，即用非线性Ｇａｌｅｒｋｉｎ谱元法对空间变量进行离散。     

功率失配误差限的几种表达方式

不确定度评定中常需对功率失配的不确定度进行评定,这就需要我们了解其误差限。实际情况中,有多种功率失配误差限的表达方式,它们的本质相同,形式不同,故在此做一下分析和总结。     

加罚纳维尔——斯托克斯方程的全离散非线性伽辽金方法

讨论了非线性伽辽金方法全离散格式用于加罚纳维尔－斯托克斯方程，这里用到了近似惯性流形方法和算子分裂方法，并证明了方法的收敛性和误差估计。     

冻结与解浆过程热分析的Galerkin方法

本文建立了二维轴对称冻结问题的Ｇａｌｅｒｋｉｎｇ该有限元数值分析法,利用该方法可分析一维问题及具有轴对称特性的任何复杂形状和复杂换热条件４的二维冻结及解冻问题。证明该方法具有精度高,收敛速度快和稳定性好的特点,是处理非线性问题的有效方法。     

非线性Galerkin方法在梁的非线性动力学性态分析中的应用

本文将非线性Ｇａｌｅｒｋｉｎ方法引入到梁的非线性动力学性状分析之中，首先，将描述梁振动的非线性偏微分方程转化为三个不同的离散化模型，其中模型Ⅱ是基于非线性Ｇａｌｅｒｋｉｎ方法得到的，它由一组常微分方程和一组代数方程组成，其次，对两组不同的轴向力，分别计算分析了上述三个模型的长期性态（时间历程，频谱，相平面图）最后，对所得结果进行了讨论。     

Helmholtz方程基于变限积分法的数值求解

Helmholtz方程是一类描述电磁波的椭圆型偏微分方程,在力学、声学和电磁学等领域应用广泛。为了消除因高波数引起的污染效应,数值求解Helmholtz方程的传统方法是对网格进行加密,网格加密不仅增加了时间复杂度,且离散后的矩阵通常是病态的。因此,寻求对任意波数都有效的方法是必要的。在有限体积法的基础上,引入变限因子,将微分方程完全转换成积分方程,利用一元三点和二元九点Lagrange插值公式,构造含三对角矩阵的离散格式,分别对一维和二维Helmholtz方程进行变限积分法的数值求解。该方法适用于任意波数,求解过程物理意义明确,数值格式简单。对于一维Helmholtz方程研究了变限因子对误差的影响,利用Taylor展式及Lagrange插值余项公式进行误差估计,证明离散格式的截断误差达到二阶。数值实例表明该离散格式的变限因子和步长相等时,误差阶较低。对二维Helmholtz方程,探究不同波数对数值解的影响,证明离散格式的截断误差达到三阶。数值实例表明,对于不同的波数,数值格式都有较好的精度,高波数没有引起污染效应。     

激光测振仪误差限的测量不确定度

介绍了评价激光测振仪误差限指标时,测量结果的不确定度分析和评价过程;讨论了影响评价结果不确定度的几个主要误差来源,包括信号源误差、测量仪器的测量误差、测量重复性的影响等等.在一个实际评价例子上,给出了误差限指标不确定度分析和评价结果;该过程及结论可应用在对于计量标准进行误差限指标的不确定度分析上,也可用于估计误差限指标本身的测量不确定度.     

对JJG577—94中基本误差限和检定流量点规定的探讨

新规程ＪＪＧ５７７－９４中的基本误差限规定与标准不符，检定Ｑｍｉｎ流量点的规定与实际情况不符。建议修改。     

基于多重有限体积法解决含有耗散项的双曲扩散问题

双曲扩散方程在数学上是一类重要的偏微分方程,在众多工程领域中有着广泛的应用．其常用于描述声波和电势场中电流的传播问题,也用于模拟计算流体力学中的对流扩散以及热传导模型．本文研究了一类具有耗散项的双曲扩散方程,并通过数值方法对其初边值问题进行求解．针对已有的有限体积法在求解该问题时精度无法提高的问题,本文基于变限积分的方法提出了新的高精度有限体积格式,并利用Fourier分析法得到其离散格式无条件稳定的结论,最后利用数值实验证实了理论分析结果．     

A posteriori error estimates and adaptive procedures for the meshless Galerkin boundary node method for 3D potential problems

The Galerkin boundary node method (GBNM) is a boundary only meshless method that combines variational formulations of boundary integral equations with the moving least-squares approximations. This paper presents the mathematical derivation of a posteriori error estimates and adaptive refinement procedures for the GBNM for 3D potential problems. Two types of error estimators are developed in detail. One is a perturbation error estimator that is formulated based on the difference between numerical solutions obtained using two successive nodal arrangements. The other is a projection error estimator that is formulated based on the difference between the GBNM solution itself and its L²-orthogonal projection. The reliability and efficiency of both types of error estimators is established. That is, these error estimators are proven to have an upper and a lower bound by the constant multiples of the exact error in the energy norm. A localization technique is introduced to accommodate the non-local property of integral operators for the needed local and computable a posteriori error indicators. Convergence analysis results of corresponding adaptive meshless procedures are also given. Numerical examples with high singularities illustrate the theoretical results and show that the proposed adaptive procedures are simple, effective and efficient.     

自然对流问题两重网格算法的残量型后验误差估计(英文)

本文得到了自然对流问题基于牛顿迭代两重网格算法的残量型后验误差估计.相对于标准有限元一层方法的后验误差估计,牛顿迭代两重网格算法的后验误差估计多了一些额外项.通过研究这些额外项的渐近行为,本文得到了这些额外项在误差估计中所起的作用.对于牛顿迭代两重网格方法的最优粗细网格匹配尺寸,这些额外项的收敛阶不高于离散解的收敛阶.数值算例验证了理论分析结论.     

一种用间接法推定摄像机光谱特性的误差特性方法

本文提出一种利用间接法来推定摄像机光谱特性的误差特性新方法。介绍了这种方法的原理，给出了误差特性表达式。利用最小二乘法还推出了误差特性的估算公式。     

一类矩阵下TOR迭代法的误差界

本文在方程组Ax=b的系数矩阵A具有相容秩序及对称正定的条件下。利用δk=x^k-x^(k-1)和δk 1=x^(k 1)-x^k的范数及内积得到了TOR迭代法的误差向量εk=x-x^k的范数的一个上界。     

Numerical analysis of dissolution processes in cementitious materials using discontinuous and continuous Galerkin time integration schemes

The present paper is concerned with the numerical integration of non‐linear reaction–diffusion problems by means of discontinuous and continuous Galerkin methods. The first‐order semidiscrete initial value problem of calcium leaching of cementitious materials, based on a phenomenological dissolution model, an electrolyte diffusion model and the spatial p‐finite element discretization, is used as a highly non‐linear model problem. A p‐finite element method is used for the spatial discretization. In the context of discontinuous Galerkin methods the semidiscrete mass balance and the continuity of the primary variables are weakly formulated within time steps and between time steps, respectively. Continuous Galerkin methods are obtained by the strong enforcement of the continuity condition as special cases. The introduction of a natural time co‐ordinate allows for the application of standard higher order temporal shape functions of the p‐Lagrange type and the well‐known Gauss–Legendre quadrature of associated time integrals. It is shown, that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p‐Galerkin methods. Selected benchmark analyses of calcium dissolution demonstrate the robustness of these methods with respect to pronounced changes of the reaction term and non‐smooth changes of Dirichlet boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Meshless Galerkin least-squares method

Collocation method and Galerkin method have been dominant in the existing meshless methods. Galerkin-based meshless methods are computational intensive, whereas collocation-based meshless methods suffer from instability. A new efficient meshless method, meshless Galerkin lest-squares method (MGLS), is proposed in this paper to combine the advantages of Galerkin method and collocation method. The problem domain is divided into two subdomains, the interior domain and boundary domain. Galerkin method is applied in the boundary domain, whereas the least-squares method is applied in the interior domain.The proposed scheme elliminates the posibilities of spurious solutions as that in the least-square method if an incorrect boundary conditions are used. To investigate the accuracy and efficiency of the proposed method, a cantilevered beam and an infinite plate with a central circular hole are analyzed in detail and numerical results are compared with those obtained by Galerkin-based meshless method (GBMM), collocation-based meshless method (CBMM) and meshless weighted least squares method (MWLS). Numerical studies show that the accuracy of the proposed MGLS is much higher than that of CBMM and is close to, even better than, that of GBMM, while the computational cost is much less than that of GBMM.Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Foundation of China with grant number 10172052.     

A priori and a posteriori analysis of the meshless Galerkin boundary node method for three-dimensional elasticity

The meshless Galerkin boundary node method is presented in this paper for boundary-only analysis of three-dimensional elasticity problems. In this method, boundary conditions can be implemented directly and easily despite the employed moving least-squares shape functions lack the delta function property, and the resulting system matrices are symmetric and positive definite. A priori error estimates and the consequent rate of convergence are presented. A posteriori error estimates are also provided. Reliable and efficient error estimators and an efficient and convergent adaptive meshless algorithm are then derived. Numerical examples showing the efficiency of the method, confirming the theoretical properties of the error estimates, and illustrating the capability of the adaptive algorithm, are reported.     

粘性不可压流动的全离散非线性Galerkin方法

这篇文章讨论了有限元情形下，粘性不可压流动的全离散非线性Ｇａｌｅｒｋｉｎ方法，此外，给出了用非线性Ｇａｌｅｒｋｉｎ方法进行的数值试验结果，和通常的Ｇａｌｅｒｋｉｎ方法比较，非线性Ｇａｌｅｒｋｉｎ方法是一种稳定性好，计算量少以及逼近精度高的数值方法。     

不可压渗流驱动问题混合有限元/间断有限元耦合格式的误差分析

多孔介质中渗流驱动问题与环境污染和油藏开采等问题密切相关,是当今的研究热点.对具有分子扩散和弥散效应的不可压渗流驱动问题,本文用混合有限元/间断有限元耦合格式来求解,即用混合有限元方法求解压力方程,用对称内罚间断有限元方法逼近浓度方程.运用比剪切算子更为便捷的归纳假设和插值投影,导出了先验hp误差估计.     

Iterative solutions for implicit Time Discontinuous Galerkin methods applied to non-linear elastodynamics

 Time Discontinuous Galerkin methods require the factorization of a matrix larger than that exploited in standard implicit schemes. Therefore, they lend themselves to implementations based on predictor-multicorrector solution algorithms. In this paper, various convergent and computationally efficient iterative methods implemented in the unknown displacements for determining the solution of non linear systems are proposed. The iterative solutions presented here differ from those implemented in the unknown velocities in that they are computationally superior. The results of numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements which are designed to evaluate the efficacy of these iterative methods with non-linear systems, show a low-computational expense when compared to earlier iterative schemes. Received: 27 May 2002 / Accepted: 28 January 2003 The financial support from the Italian Ministry for Education, Universities and Research (MIUR) is acknowledged. However, opinions expressed in this paper are those of the writers, and do not necessarily reflect the views of the sponsoring agency.