非线性色散耗散波动方程双线性元的高精度分析

针对一类非线性色散耗散波动方程研究了双线性元逼近.基于该元的高精度分析和插值后处理技巧,对于半离散格式,在精确解的合理正则性假设下得到了H~11模意义下最优误差估计及超逼近性和超收敛结果.同时,通过构造一个新的外推格式,导出了具有三阶精度的外推解.最后,建立了一个全离散逼近格式及研究其解的超逼近性.     

双曲积分微分方程的各向异性非协调有限元逼近

讨论了双曲积分微分方程在半离散格式下的一类各向异性非协调有限元逼近,得到了与传统有限元方法相同的最优误差估计和超逼近性质.同时利用插值后处理技术得到了整体超收敛结果.     

电报方程的类Wilson非协调有限元分析

本文在矩形网格上讨论了半离散和全离散格式下电报方程的类Wilson非协调有限元逼近.利用该元在H1模意义下O(h2)阶的相容误差结果,平均值理论和关于时间t的导数转移技巧得到了超逼近性.进而,借助于插值后处理方法导出了超收敛结果.又由于该元在H1模意义下的相容误差可以达到O(h3)阶,构造了新的外推格式,给出了比传统误差估计高两阶的外推估计.最后,对于给出的全离散逼近格式得到了最优误差估计.     

Sobolev方程的一类各向异性非协调有限元逼近

在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.     

非线性sine-Gordon方程的双线性元分析及外推

研究双线性元对一类非线性sine-Gordon方程的有限元逼近.利用该元的高精度结果和对时间t的导数转移技巧,得到了H~1模意义下的超逼近性.进一步地,通过运用插值后处理技术,给出了H~1模意义下的超收敛结果.与此同时,通过构造一个新的外推格式,导出了与线性问题情形相同的三阶外推解.最后给出了一种全离散逼近格式下的最优误差估计.     

三维二次有限元梯度最大模的超逼近

作者证明了在一致四面体剖分下三维二次有限元的第一型弱估计,并给出了三维导数离散Green函数的估计,由此得到了四面体二次元梯度最大模的超逼近．通过这个超逼近还可以获得四面体二次元梯度最大模的超收敛．     

张量积二次长方体有限元梯度最大模的超逼近

对于某种三维椭圆边值问题,本文给出了长方体剖分下张量积二次长方体有限元的第一型弱估计以及离散导数Green函数的W^1,1半范估计,利用这两个估计本文获得了张量积二次长方体有限元梯度最大模的超逼近．进而,由超逼近也可以得到这种有限元梯度最大模的超收敛．     

细菌模型的非协调有限元分析

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.     

非线性Benjamin-Bona-Mahony方程一个新的低阶混合元方法[英文]

基于双线性元和零阶R-T元, 建立了非线性Benjamin-Bona-Mahony (BBM)方程的一个新的低阶混合元方法. 借助积分恒等式技巧, 得到了一个对超逼近分析比较重要的误差估计. 对于半离散格式, 证明了解的存在性, 唯一性和稳定性, 然后得到了精确解~$u$在$H^1$模意义下和压力变量~ $\vec{p}=\nabla u_t$在 $L^2 $模意义下具有$O(h^2)$ 的超逼近和超收敛结果. 对于向后欧拉和 Crank-Nicolson 全离散格式, 分别探讨了解的稳定性, 且在对时间步长没有任何限制的前提下得到了超逼近结果.     

拟线性粘弹性方程新H~1-Galerkin最低阶混合元格式的高精度分析

利用双线性元和零阶Raviart-Thomas元,针对拟线性粘弹性方程建立新的H~1-Galerkin混合元逼近格式.在半离散格式下,给出原始变量u的H~1模和应力=?ut的H(div;?)模的超逼近性和超收敛结果.同时,导出向后欧拉格式和Crank-Nicolson-Galerkin格式的最优误差估计.最后,通过数值算例表明逼近格式是有效的.     

On the boundedness and unboundedness of external polyhedral estimates for reachable sets of linear differential systems

The boundedness and unboundedness properties of external polyhedral (paralle-lepiped-valued) estimates are investigated for reachable sets of linear differential systems with a stable matrix. Boundedness and unboundedness criteria on an infinite time interval are presented for two types of estimates (“touching” estimates, which were introduced earlier, and estimates with constant orientation matrix). Conditions for the system matrix and bounding sets are given under which there are bounded estimates among the estimates of the mentioned types, under which there are unbounded estimates, and under which all the estimates are bounded or all the estimates are unbounded. In terms of the exponents of the estimates, the possible rate of their growth is described. For two-dimensional systems, the classification and comparison of possible situations of the boundedness or unboundedness for estimates of both types are given and boundedness criteria for estimates with special (orthogonal and “quasi-orthogonal”) constant orientation matrices are found. Results of numerical modeling are presented.     

Asymptotic normality of cumulant spectral estimates

The paper considers higher-order cumulant spectral estimates obtained by directly Fourier transforming weighted cumulant estimates. Such estimates computationally are different from those based on the finite Fourier transform. These estimates can be looked at continuously as well as directly on submanifolds. The estimates of cumulants are based on unbiased moment estimates. Asymptotic normality is obtained for these estimates and is based on a strong mixing condition and only a finite number of cumulant summability conditions.     

Window estimates of location and scale with applications to the cauchy distribution

Location and scale parameters are estimated via “window estimates”. The consistency and asymptotic normality of the estimates are established. The special case of the Cauchy distribution is considered, where the estimates are shown to have the same asymptotic distribution as the maximum-likelihood estimates. Additional applications are given for the Pearson type-VII distributions. The estimates have the advantages of ease of computation and high asymptotic efficiencies for certain heavy-tailed distributions.     

A new estimate of the parameters in linear mixed models

In linear mixed models, there are two kinds of unknown parameters: one is the fixed effect, the other is the variance component. In this paper, new estimates of these parameters, called the spectral decomposition estimates, are proposed, Some important statistical properties of the new estimates are established, in particular the linearity of the estimates of the fixed effects with many statistical optimalities. A new method is applied to two important models which are used in economics, finance, and mechanical fields. All estimates obtained have good statistical and practical meaning.     

Generalized estimates for performance sensitivities of stochastic systems

Three kinds of estimates for performance sensitivities (gradients, Hessians etc.) of stochastic systems are introduced. These estimates are given in general operator form. Their convergence conditions and rate of convergence are presented. Particular attention is given to estimates obtained from a single sample path. Various examples of estimates are considered.     

Error estimates in elastoplasticity using a mixed method

In this paper, a mixed formulation and its discretization are introduced for elastoplasticity with linear kinematic hardening. The mixed formulation relies on the introduction of a Lagrange multiplier to resolve the non-differentiability of the plastic work function. The main focus is on the derivation of a priori and a posteriori error estimates based on general discretization spaces. The estimates are applied to several low-order finite elements. In particular, a posteriori estimates are expressed in terms of standard residual estimates. Numerical experiments are presented, confirming the applicability of the a posteriori estimates within an adaptive procedure.     

Solution Estimates for Nonlinear Nonautonomous Evolution Equations in Spaces with Normalizing Mappings

Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.     

The Construction and Properties of Boundary Kernels for Smoothing Sparse Multinomials

In recent years several authors have investigated the use of smoothing methods for sparse multinomial data. In particular, Hall and Titterington (1987) studied kernel smoothing in detail. It is pointed out here that the bias of kernel estimates of probabilities for cells near the boundaries of the multinomial vector can dominate the mean sum of squared error of the estimator for most true probability vectors. Fortunately, boundary kernels devised to correct boundary effects for kernel regression estimators can achieve the same result for these estimators. Properties of estimates based on boundary kernels are investigated and compared to unmodified kernel estimates and maximum penalized likelihood estimates. Monte Carlo evidence indicates that the boundary-corrected kernel estimates usually outperform uncorrected kernel estimates and are quite competitive with penalized likelihood estimates.     

Nonparametric estimation of the location and scale parameters based on density estimation

Summary By representing the location and scale parameters of an absolutely continuous distribution as functionals of the usually unknown probability density function, it is possible to provide estimates of these parameters in terms of estimates of the unknown functionals. Using the properties of well-known methods of density estimates, it is shown that the proposed estimates possess nice large sample properties and it is indicated that they are also robust against dependence in the sample. The estimates perform well against other estimates of location and scale parameters.     

增长曲线模型回归系数线性估计的泛容许性

本文讨论增长曲线模型回归系数的线性估计的容许性.我们给出了回归系数线性估计的泛容许性定义,并在某些线性估计类中得到了泛容许估计的充要条件.