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本文研究对称椭圆特征值问题的有限元后验误差估计,包括协调元和非协调元,具有下列特色:(1)对协调/非协调元建立了有限元特征函数uh的误差与相应的边值问题有限元解的误差在局部能量模意义下的恒等关系式,该边值问题的右端为有限元特征值λh与uh的乘积,有限元解恰好为uh.从而边值问题有限元解在能量模意义下的局部后验误差指示子,包括残差型和重构型后验误差指示子,成为有限元特征函数在能量模意义下的局部后验误差指示子.(2)讨论了协调有限元特征函数的基于插值后处理的梯度重构型后验误差估计,对有限元特征函数的导数得到了最大模意义下的渐近准确局部后验误差指示子. 相似文献
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二阶特征值问题的非协调元逼近 总被引:1,自引:0,他引:1
本文以非协调三角形线性元为例,讨论了二阶特征值问题的非协调有限元逼近,基于二阶变分问题非协调有限元逼近的有关分析结果,不仅得到了特征值逼近解的误差估计,而且得到了特征函数逼近解的最优的L~2-误差估计和拟最优的L~∞-误差估计。 相似文献
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非协调板元的一般性误差估计式 总被引:8,自引:0,他引:8
1.引言 薄板弯曲问题对应于4阶椭圆边值问题,协调有限元求解此问题需要单元具有C~1连续性,这难于构造且应用不便,因此求解该问题主要应用非协调元.当非协调板元不具有 C0连续性时,标准能量模误差估计是 ,这一结果不理想,因为对一般的区域,甚至是凸多边形区域,真解只能属于 H3.近年来,企图将真解属于 H4的假定改为真解属于 H3的研究引起重视.针对最简单的三角形非协调板元-Morley元,石钟慈[2]在 H3假定下,直接利用非协调元分析技巧得到弯距和转角的误差估计式.本文将[2]的结果一般化,同时通过修… 相似文献
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将非协调元应用于描述细菌传播的反应扩散方程组的初边值问题.借助单元的一些特性和非协调误差估计技巧,分别在半离散和全离散有限元格式下,研究了其数值解与精确解的误差估计,得到了最优的误差估计以及超逼近结果. 相似文献
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基于EQrot1非协调元的两个特殊性质:一是诱导的有限元插值算子与传统的Ritz投影是一致的;二是当所考虑问题的精确解属于H3(Ω)时,其相容误差为O(h2)阶,比插值误差高一阶.本文对非线性Sine-Gordon方程提出一个新的二阶全离散格式,给出收敛性分析和最优阶误差估计.最后,讨论本文的结果对另外一些著名的非协调元的应用. 相似文献
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本文研究了正方体区域上Qrot1非协调元渐近展开式.利用林群、吕涛等提出的有限元误差渐近展开法,获得了正方体区域上Qrot1非协调元特征值的误差渐近展开式.理论分析和数值实验结果表明三维Qrot1非协渊元特征值外推公式是有效的,可以把特征值的精度从二阶提高到四阶. 相似文献
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Stokes型积分微分方程的质量集中各向异性非协调有限元分析 总被引:2,自引:0,他引:2
本文将Crouzeix-Raviart型非协调三角形元应用到发展型Stokes积分微分方程,给出了其质量集中非协调有限元逼近格式.在各向异性网格下,导出了速度的L2模和能量模及压力的L2模的误差估计. 相似文献
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本文研究了正方体区域上Q1rot非协调元渐近展开式.利用林群、吕涛等提出的有限元误差渐近展开法,获得了正方体区域上Q1rot非协调元特征值的误差渐近展开式.理论分析和数值实验结果表明三维Q1rot非协调元特征值外推公式是有效的,可以把特征值的精度从二阶提高到四阶. 相似文献
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Samuel Albert Bernardo Cockburn Donald A. French Todd E. Peterson. 《Mathematics of Computation》2002,71(237):49-76
A new upper bound is provided for the L-norm of the difference between the viscosity solution of a model steady state Hamilton-Jacobi equation, , and any given approximation, . This upper bound is independent of the method used to compute the approximation ; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of . Numerical experiments investigating the sharpness of the a posteriori error estimate are given.
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New improved error bounds for the linear complementarity problem 总被引:1,自引:0,他引:1
New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a best error bound emerges from our comparisons as the sum of two natural residuals.This material is based on research supported by Air Force Office of Scientific Research Grant AFOSR-89-0410 and National Science Foundation Grant CCR-9101801. 相似文献
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Many processes in the sciences and in engineering are modelled by dynamical systems and—in discretized version—by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples. 相似文献
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P. Le Bars 《Journal of Combinatorial Theory, Series A》2006,113(8):1771-1782
The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code. 相似文献
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基于空间分解变换的模糊错误矩阵方程求解 总被引:1,自引:0,他引:1
模糊错误逻辑对现实世界的对象用(u,x)表示为((U,S(t),■T(t),L(t)),(x(t)=f((u(t),■),GU(t)),GU(t)),用模糊错误变换矩阵可以表示分解、相似、增加、置换、毁灭、单位变换等6种变换方法,本论文基于求解方程XA′=B,针对■的分解,研究了基于空间分解变换的错误矩阵方程求解。以期从矩阵方程求解的角度对错误转化规律进行探索研究。 相似文献
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Dang Duc Trong 《Journal of Mathematical Analysis and Applications》2005,312(1):93-104
We study the nonhomogeneous heat equation under the form ut−uxx=φ(t)f(x), where the unknown is the pair of functions (u,f). Under various assumptions about the function φ and the final value in t=1, i.e., g(x), we propose different regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For φ?0 the solution is unique. 相似文献
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进行错误识别,首先我们需要研究识别的对象.因此,研究首先将错误识别对象分为识别状态、真是状态、应该状态和目标状态等四种状态,并且讨论了几种类型之间的关系.最后运用矩阵逻辑方程求解了识别状态转化为目标状态的转化方式. 相似文献
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Fabio Camilli Italo Capuzzo Dolcetta Diogo A. Gomes 《Applied Mathematics and Optimization》2008,57(1):30-57
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several
error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal
control setting and as well as in the calculus of variations setting.
D.G. was partially supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems through FCT Program POCTI/FEDER
and by grant POCI/FEDER/MAT/55745/2004. 相似文献
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In this paper we establish a stability result and an error estimate of weak solutions for the initial-boundary value problem of a generalized thin film equation and also obtain some higher regularity results for weak solutions. 相似文献