共查询到19条相似文献,搜索用时 674 毫秒
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在许多有限元计算中经常在求得近似解后还要求得到近似的解的导数.如在弹性计算中,如何从计算得到的位移近似解较好地计算应力早已被研究多年.如果计算中包含直接对近似解求导数,必然会丧失部分精度,得不到满意的结果.特别,若近似解为分片常数函数,则根本无法从直接求导数得到应力的近似值.Babuska和 Miller提出了所谓“提取法”,即利用推导出来的提取公式来求解的导数的近似值,以得到与近似解本身同 相似文献
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1.引言 我们知道Poisson方程和平面弹性问题的解的导数的近似值可以通过所谓提取公式得到,而不必对近似解直接求导数.这样我们可以得到具有与近似解本身同阶精度的导数的近似值.这一方法已被用于基于插值误差的后验误差估计及相应的自适应有限元方法中本文将这一方法应用于Stokes问题的有限元逼近,从Stokes方程的解的 相似文献
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陈双 《数学的实践与认识》2014,(23)
二分法和牛顿法求非线性方程根的近似值已列入中学课程.但它背后的哲学原理(相对真理)/(绝对真理)=0.9,只在林群的新书中说到2(1/2)时提出来.根据教学需要,通过(不足近似值)/(过剩近似值)=0.9等数值化的公式,来刻画根的近似过程.可以清楚地看到,随着小数点后9的个数的增加,近似解和真实解的误差在不断减小.因此0.9数值化系列公式也可以看做是误差估计的另一种表型形式. 相似文献
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1引 言积分的计算是自然科学中的一个基本问题.当积分的精确值不能求出时,数值积分就变得越来越重要了.数值积分的基本思想是直接利用被积函数(及其导数)在若干点处的函数值作线性组合得到积分的近似值.外推算法是一种可以提高数值计算精度的技巧,它利用几个精度较低的近似值作线性组合得到精度较高的近似值.定积分的复化求积公式及其外推算法可见[1]-[7],二重积分的复化求积公式可见[8,9,10],三重积分的复化求积公式可见[11,12]. 相似文献
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考虑由未知二元函数的近似值计算其Laplace算子与二阶混合偏导数的问题,给出稳定逼近Laplace算子与二阶混合偏导数的两类Lanczos方法,其逼近精度分别为O(δ~(1/2))和O(δ~(2/3)),其中δ是近似函数的误差水平. 相似文献
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拟线性伪双曲型方程的变网格有限元解法 总被引:4,自引:1,他引:3
芮洪兴 《高等学校计算数学学报》1988,(4)
其中Ω为R~m中有界凸域。这类方程有其实际的物理背景,例如,动物神经系统中生物电讯息传播过程,就可以用一维伪双曲型方程来描述。对于问题(1.1)解的正则性,已有不少作者作了研究,且提出了求解的数值方法。本文提出了变网格有限元格式来求其近似解。这类方法已被不少作者采用,这样我们可以在不同的时间层采用不同的网格,使计算结果更好。采用本文提出的方法,不但可以求得精确解x的近似值,而且可以求得u_t的近似值。在网格变动次数M=0(1/h)时,有限元解对精确解的 相似文献
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文[1]介绍了求无理数q~(1/p)的近似值可按下操作进行:先选定a_0作为q~(1/p)的初始近似值,再求这样a_n就可作为q~(1/p)的近似值.这个递推公式是如何获得的呢?我们可借助于新教材中的导数知识对学生进行解释. 相似文献
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李立康 《高等学校计算数学学报》1982,(2)
配置法可用来求各种类型方程的数值解。与Galerkin方法相比,它可避免计算数值积分。Douglas等人讨论了用配置法求抛物型方程初边值问题数值解的误差。本文讨论用配置法求具有间断系数抛物型方程数值解的误差。在求近似解时,允许系数的间断点与分割点不重合。在中Douglas用配置法求热传导方程的数值解,近似解空间由属于C~1(I)中的分段四次多项式全体组成,得到在分割结点处的误差有 相似文献
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Xiao-bo Liu 《计算数学(英文版)》1999,17(5):475-494
1.IntroductionInteriorerrorestimatesforfiniteelementdiscretizations(conforming)werefirstintroducedbyNitscheandSchatz[14]forsecondorderscalarellipticequationsin1974.Theyprovedthatthelocalaccuracyofthefiniteelementapproximationisboundedintermsoftwofact... 相似文献
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静力分析的一般随机摄动法 总被引:7,自引:0,他引:7
本文对向量值和矩阵值函数的不确定结构的静力响应和可靠性进行了研究。基于Kronecker代数和摄动理论导出了随机结构的有限元分析方法,随机变量和系统导数很方便地排列到2D矩阵中,给出了一般的数学表达式. 相似文献
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Xiaobo Liu 《Numerische Mathematik》1996,74(1):49-67
Summary. Interior error estimates are derived for a wide class of nonconforming finite element methods for second order scalar elliptic
boundary value problems. It is shown that the error in an interior domain can be estimated by three terms: the first one measures
the local approximability of the finite element space to the exact solution, the second one measures the degree of continuity
of the finite element space (the consistency error), and the last one expresses the global effect through the error in an
arbitrarily weak Sobolev norm over a slightly larger domain. As an application, interior superconvergences of some difference
quotients of the finite element solution are obtained for the derivatives of the exact solution when the mesh satisfies some
translation invariant condition.
Received December 29, 1994 相似文献
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Eusebius Doededl 《Journal of Difference Equations and Applications》2013,19(5-6):152-161
Algorithmic aspects of a class of finite element collocation methods for the approximate numerical solution of elliptic partial differential equations are described Locall for each finite element the approximate solution is a polynomial. polynomials corresponding toadjacent finite elements need not match continuously but their values and noumal derivatives match at a discrete set of points on the common boundary.High order accuracy can be attained by increasing the number of mathching points and the number of colloction points for each finite element.Forlinear equations the collocation methods can be equivalently definde as generlized finite difference methods. The linear (or linearzed )equations that arise from the discretization lend themselves well to solution by the methods of the methods nested dissection.An implememtation is described and some numerical results are givevn. 相似文献
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Roman Kohut 《Applications of Mathematics》2018,63(6):603-628
The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between elements of matrices of the coarse and fine problems can be derived. By generalization of these formulae, we obtain an overlapping aggregation technique for the construction of a coarse space with smoothed basis functions. The numerical tests are presented at the end of the paper. 相似文献
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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. 相似文献
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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. 相似文献
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This paper is devoted to the introduction of a mixed finite element for the solution of the biharmonic problem. We prove optimal rate of convergence for the element. The mixed approach allows the simultaneous approximation of both displacement and tensor of its second derivatives. 相似文献