Stokes问题Q_2-P_1混合元外推方法

考虑Stokes问题的有限元解与精确解插值的Q2-P1混合元的渐近误差展开和分裂外推.首先利用积分恒等式技巧确定了微分方程精确解与有限元插值之间积分式的主项,其次再借助插值后处理和分裂外推技术,得到了比通常的误差估计提高两阶的收敛速度.     

一个新高次Wilson元及其收敛性分析

给出一个新的高次Wilson元,证明了它的收敛性,获得了解的超逼近性质,并且利用插值后处理技术得到了有限元解的整体超收敛.在此基础上还得到了解的后验误差估计.     

Raviart-Thomas混合元的超收敛

考虑二阶椭圆方程Dirichlet边值问题在正则矩形网格上k阶RaviartThomas混合有限元的超收敛.对有限元解经插值处理后,与通常的有限元最优误差估计相比,收敛速度提高了两阶.     

变系数抛物方程的有限元强校正格式

本文利用投影型插值和Ritz-Volterra投影研究一维变系数抛物方程的有限元方法,直接得到导数和位移的一个强校正格式.对于有限元解,分别对应力和位移获得整体的hk＋2和hk＋3阶的强结果.     

多孔介质中非Fick流的校正方法

本文首先给出H~1-模意义下多孔介质中非Fick流的矩形双线性元的渐进误差展开,进而通过插值后处理方法得到一种插值校正格式来提高有限元近似解的精度.     

特征值问题协调/非协调有限元后验误差分析

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.     

拟线性双相滞热传导方程的双线性元高精度分析及外推

研究一类拟线性双相滞热传导方程的双线性有限元逼近,利用该元的Ritz投影和插值相结合的技巧,并结合高精度分析和插值后处理技术分别导出了半离散和全离散格式的超逼近和超收敛结果.同时通过构造合适的辅助问题,对半离散格式导出了具有三阶精度的外推解.     

拟线性Sobolev方程Carey元解的高精度分析

在一种半离散格式下讨论了拟线性Sobolev方程Carey元的超收敛及外推.根据Carey元的构造证明了其有限元解的线性插值与三角形线性元的解相同,再结合线性元的高精度分析和插值后处理技巧导出了超逼近和整体超收敛及后验误差估计.与此同时,根据线性元的误差渐近展开式,构造了一个新的辅助问题,得到了比传统的有限元误差高三阶的外推结果.     

对流扩散反应方程的局部投影稳定化连续时空有限元方法

本文将局部投影稳定化(LPS)方法和连续时空有限元方法相结合研究对流扩散反应方程,给出稳定化连续时空有限元离散格式.与传统的时空有限元研究思路不同,时间方向利用Lagrange插值多项式,解耦时间和空间变量,降低时空有限元解的维数,具有减少计算量和简化理论分析的优点.通过引入Legendre多项式给出了有限元解的稳定性...     

解抛物型方程的半离散精细积分法

本讨论抛物型方程混合问题的解法．提出在有限元半离散过程后，用精细积分法获得一个较好的解，并且分析了这种方法的误差，证明了用这种方法和二次插值，在节点上有O(h^4)的超收敛性．     

On the complexity of solving feasible systems of linear inequalities specified with approximate data

An algorithm that gives an approximate solution of a desired accuracy to a system of linear inequalities specified with approximate data is presented. It uses knowledge that the actual instance is feasible to reduce the data precision necessary to give an approximate solution to the actual instance. In some cases, this additional information allows problem instances that are ill-posed without the knowledge of feasibility to be solved.The algorithm is computationally efficient and requires not much more data accuracy than the minimal amount necessary to give an approximate solution of the desired accuracy. This work aids in the development of a computational complexity theory that uses approximate data and knowledge.     

On the equivalence of neural nets and fuzzy expert systems

We show, under the assumptions described in the paper, that: (1) we can approximate a neural net to any degree of accuracy using a fuzzy expert system; and conversely (2) we may approximate a fuzzy expert system to any degree of accuracy with a neural net.     

L-统计量的Edgeworth展开和随机加权逼近

文［１］讨论了Ｌ－统计量的一种能达到Ｏ１√ｎ精确度的随机加权逼近,本文则给出了Ｌ－统计量的Ｅｄｇｅｗｏｒｔｈ展开和一种能达到ｏ１√ｎ精确性的新的随机加权逼近     

Von-Mises统计量的Edgeworth展开和随机加权逼近

文［１］讨论了Ｖｏｎ－Ｍｉｓｅｓ统计量的一种能达到Ｏ１ｎ的精确性的随机加权逼近，本文则给出了这种统计量的一阶Ｅｄｇｅｗｏｒｔｈ展开和一种能达到ｏ１ｎ的精确性的新的随机加权逼近．     

The exact and approximate method in mechanical system's analysis

The main aim of this work is to present results of the mechanical system's analysis based on the exact and approximate Galerkin's methods. The considered system is the flexural vibrating one-dimension bending beam. The exact and approximate method were used to assign the dynamic flexibility of the considered system and results of this work were juxtaposed to verify the approximate method's accuracy. The correction coefficients were introduced into the approximate method to unify results of both methods. The aim of this work was to check accuracy of the approximate method and to verify if this method may be used to mechatronic system's analysis, where it is impossible to use the exact method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation of variational eigenvalue problems

A variational eigenvalue problem in an infinite-dimensional Hilbert space is approximated by a problem in a finite-dimensional subspace. We analyze the convergence and accuracy of the approximate solutions. The general results are illustrated by a scheme of the finite element method with numerical integration for a one-dimensional second-order differential eigenvalue problem. For this approximation, we obtain optimal estimates for the accuracy of the approximate solutions.     

Dynamics of micromachined vibrating gimbal and wheel gyroscope

We deduce dynamic equations of micromachined vibrating gimbal and wheel gyroscope and give an approximate solution of enough accuracy. The comparison between the approximate solution and the solution used often in the literature is given. According to property of the approximate solution a decoupled two-axes gyroscope will be composed of two single-axes gyroscopes.     

对数正态或正态寿命型元件及系统的贮存可靠性的近似置信下限

本文给出了基于一次性检测数据的对数正态或正态寿命型元件及系统的贮存可靠性的近似置信下限的方法，并对得到的近似置信限的精度作了讨论，结果表明精度符合要求。本文还给出了数字例子。     

Newton–harmonic balancing approach for accurate solutions to nonlinear cubic–quintic Duffing oscillators

This paper presents a new approach for solving accurate approximate analytical higher-order solutions for strong nonlinear Duffing oscillators with cubic–quintic nonlinear restoring force. The system is conservative and with odd nonlinearity. The new approach couples Newton’s method with harmonic balancing. Unlike the classical harmonic balance method, accurate analytical approximate solutions are possible because linearization of the governing differential equation by Newton’s method is conducted prior to harmonic balancing. The approach yields simple linear algebraic equations instead of nonlinear algebraic equations without analytical solution. Using the approach, accurate higher-order approximate analytical expressions for period and periodic solution are established. These approximate solutions are valid for small as well as large amplitudes of oscillation. In addition, it is not restricted to the presence of a small parameter such as in the classical perturbation method. Illustrative examples are presented to verify accuracy and explicitness of the approximate solutions. The effect of strong quintic nonlinearity on accuracy as compared to cubic nonlinearity is also discussed.     

Optimal iterative perturbation technique for solving Jeffery--Hamel flow with high magnetic field and nanoparticle

In this research paper, a different semi-analytical analysis of modified magnetohydrodynamic Jeffery--Hamel flow is conducted via the newly developed technique. We use the optimal iterative perturbation method with multiple parameters to see the effects of the magnetic field and nanoparticle on the Jeffery--Hamel flow. Comparing our new approximate solutions with some earlier works proved the excellent accuracy of the newly proposed technique. Convergence analysis of the proposed method is also discussed and error estimation is given to anticipate the accuracy of higher-order approximate solutions.