非协调有限元逼近的梯度恢复型后验误差估计（英文）

本文给出二阶椭圆型方程的非协调有限元的梯度恢复型后验误差估计.后验误差估计是在Crouzeix-Raviart非协调有限单元上得到的,并且给出误差的上下界,更进一步可以证明所得的后验误差估计在拟一致网格上是渐近精确的,所以误差估计是可行的、有效的.上界证明过程依赖于"Helmholtz分解",下界证明主要依赖"bubble函数".数值结果验证了理论的正确性.     

定常Navier-Stokes方程流函数形式两重网格算法的残量型后验误差估计

运用七种两重网格协调元方法得出了不可压Navier-Stokes方程流函数形式的残量型后验误差估计．对比标准有限元方法的后验误差估计,两重网格算法的后验误差估计多了一些额外项(三线性项)．说明了这些额外项在误差估计中对研究离散解渐近性的重要性,推出了对于最优网格尺寸,这些额外项的收敛阶不高于标准离散解的收敛阶．     

一阶双曲问题间断有限元的后验误差分析

一阶双曲问题的有限元后验误差估计至今没有得到很好的解决.本文对d维区域上一阶双曲问题的k次间断有限元逼近提出了一种新的后验误差分析方法, 进而建立了间断有限元解在DG范数下(强于L₂范数)基于误差余量型的后验误差估计. 数值计算验证了本文理论分析的有效性. 本文方法也适用于其他变分问题有限元逼近的后验误差分析.     

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.     

稳态Poisson-Nernst-Planck方程的残量型后验误差估计

针对稳态的Poisson-Nernst-Planck方程研究了一种残量型的后验误差估计子,对方程的两个解-浓度和电势,都分别给出了上界和下界估计.数值实验表明,基于这种后验误差估计子构造的自适应有限元算法对于稳态的Poisson-Nernst-Planck方程是有效的.     

关于非协调Qrot1元可计算上界后验误差估计的一个注记

通过数值试验发现Ainsworth建立的非协调Qrot1元可计算上界后误差估计指示子的可靠、有效性差.参照相关文献以及根据Qrot1元的性质,在Ainsworth建立的可计算上界后验误差估计框架下对插值后处理函数的构造和选取分别作了修改和更换,并相应获得可靠且有效的可计算上界后验误差估计,给出了三个不同类型的例子及其实验结果.     

Stokes方程最优控制问题超收敛与后验估计

1 引言 Stokes方程最优控制问题在工程应用中有重要的意义,其数值方法的研究受到人们的广泛关注．本文应用重构型超收敛技术得到了超收敛结果和渐进准确的后验误差估计．应用后验误差估计我们还能进行自适应计算．     

有限元方法的后验误差估计

有限元的误差分析理论已有丰富的成果,但一般以先验估计为主。这些理论对算法评价和指导计算无疑具有重要意义。但实际计算中常要求给出误差的定量估计,先验估计一般就做不到这一点,因为其中会有如微分方程解的导数等不可计算的量。后验误差估计的研究近年来已开始受到注意。在多重网格技术中基于误差渐近展开的外推可以给出逐点意义下的后验估计。(例如见[1],[2])另一条途径是通过局部化进行能量模意义下的后验误差估计。其中对一维边值问题的研究已较成熟。[7]就常系数     

中子输运方程误差估计及自适应计算

 本文研究了全离散方法求解二维中子输运方程的有限元自适应算法, 角度变量用离散纵坐标方法展开, 空间变量用间断元方法求解. 基于间断元方法给出了空间离散的残量型后验误差估计. 在后验误差估计的基础上, 我们设计了自适应有限元算法.由残量型后验估计可以给出局部加密网格的自适应算法. 最后, 我们给出了数值算例来验证我们的理论结果.     

达尔文模型的有限元后验误差估计

在三维有界单连通区域里,当没有高频现象或电流变化不快时,达尔文模型是麦克斯韦方程组的-个很好的逼近模型.本文考虑达尔文模型的自适应算法,这种方法以有限元后验误差分析为理论基础.本文提供了基于后验误差估计子的上界估计.     

Implicit a posteriori error estimation using patch recovery techniques

We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.     

Asymptotically exact a posteriori error estimator for biquadratic elements

This paper addresses the finite element method with a posteriori error estimation for elements of degree p = 1 and p = 2. It gives the formulae for the error indicators and error estimators. Basic mathematical characterizations of the estimators are given and it is shown that the estimators for p = 1 and p = 2 have different structures. Numerical examples show the effectivity of the approach and the high quality of the estimator.     

Error estimators for advection–reaction–diffusion equations based on the solution of local problems

This paper deals with a posteriori error estimates for advection–reaction–diffusion equations. In particular, error estimators based on the solution of local problems are derived for a stabilized finite element method. These estimators are proved to be equivalent to the error, with equivalence constants eventually depending on the physical parameters. Numerical experiments illustrating the performance of this approach are reported.     

鞅差误差序列下半参数EV回归模型的近邻估计

本文研究了误差为鞅差序列的条件下的一维半参数EV回归模型.利用两步估计的方法构造了参数分量和非参数分量的近邻估计,并且分别证明了估计量的L2相合性和强相合性,从而推广了在普通半参数回归模型已有的相关结论.     

Instrumental variable approach to covariate measurement error in generalized linear models

The paper presents the method of moments estimation for generalized linear measurement error models using the instrumental variable approach. The measurement error has a parametric distribution that is not necessarily normal, while the distributions of the unobserved covariates are nonparametric. We also propose simulation-based estimators for the situation where the closed forms of the moments are not available. The proposed estimators are strongly consistent and asymptotically normally distributed under some regularity conditions. Finite sample performances of the estimators are investigated through simulation studies.     

Comparison of Different Error Indicators for Contact Problems Involving Large Elastic Strains

Finite element methods (FEMs) are flexible tools which can be applied to solve contact problems with arbitrary geometries. As in any numerical method, the solutions obtained with FEM are only approximate. Errors occur e.g. due to the choice of the ansatz space and the approximation of the geometry. In general it is necessary to automatically control the error inherited in the method to obtain reliable solutions. This is especially true in case of non-linear contact problems since geometry and contact surface can change substantially during the deformation process. Thus the refinement process needed for an accurate analysis cannot be controlled by the user beforehand. Here an adaptive FEM is developed for large strain problems of two or more deformable bodies being in contact. The main focus is the comparison of different error indicators and error estimators related to the contact problem. In detail residual based, error estimators, error indicators relying on superconvergence properties and error estimators based on duality principles are investigated. Finally, examples show the convergence behaviour of the error measures.     

A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

<正>In this paper,a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems.The key idea is to postprocess the Galerkin approximation,and the analysis shows that the postprocess improves the order of convergence.Consequently,we obtain asymptotically exact aposteriori error estimators based on the postprocessing results.Numerical examples are included to illustrate the theoretical analysis.     

Consistent estimation of coefficients in measurement error models with replicated observations

For the estimation of coefficients in a measurement error model, the least squares method utilizing original observations and averaged observations over replications provides inconsistent estimators. Based on these, consistent estimators are formulated and asymptotic properties are analyzed.     

Distributions and moments for estimators of Gini index in an exponential distribution

In this paper, we propose several estimators of Gini index of the two-parameter exponential distribution and obtain distributions and moments of the proposed estimators. The proposed estimators are shown to cosistency and will be compared in terms of the mean squared error (MSE) through Monte Carlo method.     

A posteriori finite element error estimators for indefinite elliptic boundary value problems ∗

A general construction technique is presented for a posteriori error estimators of finite element solutions of elliptic boundary value problems that satisfy a Gång inequality. The estimators are obtained by an element–by–element solution of ‘weak residual’ with or without considering element boundary residuals. There is no order restriction on the finite element spaces used for the approximate solution or the error estimation; that is, the design of the estimators is applicable in connection with either one of the h–p–, or hp– formulations of the finite element method. Under suitable assumptions it is shown that the estimators are bounded by constant multiples of the true error in a suitable norm. Some numerical results are given to demonstrate the effectiveness and efficiency of the approach.