定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

提出了定常的磁流体动力学方程的一种Galerkin-Petrov最小二乘混合元法,并导出Galerkin-Petrov最小二乘混合元解的存在性和误差估计．通过引入Galerkin-Petrov最小二乘混合有限元方法使得该方法的混合元空间之间的组合无需满足离散的Babuska-Brezzi稳定性条件,从而使得它们的混合有限元空间可以任意选取,并得到误差估计最优阶．     

对流扩散反应方程的特征分裂最小二乘方法

1引言众所周知,最小二乘混合有限元方法具有两个显著的优点:一是不必满足经典混合元要求LBB条件,因此一般的有限元空间可供选择;二是算法系统是对称正定的,从而利于问题的求解.Pehlivanov等提出了一种最小二乘混合有限元算法求解椭圆型边值问题,并给出了H~1×H(div,·)模误差估计.之后,Cai等人把此方法推广应用到带有对流和反应项的二阶偏微分方程.近年来,最小二乘方法被应用到时间相关的问题.     

非定常的热传导-对流问题的Petrov最小二乘混合有限元法及其误差估计

文提出了非定常的热传导-对流方程的一种Petrov最小二乘混合有限元法.Petrov最小二乘混合有限元法可以回避Babuska-Brezzi条件的约束,使得有限元空间可以自由地选择并获得最优阶的误差估计.     

定常的Navier-Stokes方程的非线性Galerkin/Petrov最小二乘混合元法

给出定常的Navier-Stokes方程的一种非线性Galerkin/Petrov最小二乘混合元法，该方法是将余量形式的Petrov最小二乘方法与非线性Galerkin混合元结合起来，使得速度和压力的混合元空间无需满足离散的Babuska-Brezzi稳定性条件，从而使得它们的有限元空间可以任意选择。并证明该方法的解的存在唯一性和收敛性。     

部分线性混合效应模型的有效估计（英文）

本文我们给出部分线性混合效应模型的有效估计方法.首先,我们使用广义最小二乘估计和B样条方法去估计未知量,然后利用惩罚最小二乘方法得到随机效应项的估计.接着我们还考虑了方差分量的估计.和现有的方法相比,我们的方法表现更好.此外,我们还给出了估计量的渐近性质.最后,模拟研究被用来评价我们的估计方法的表现.     

退化椭圆问题的最小二乘混合元逼近

１．引言我们将考虑具有退化系数的椭圆问题其中 Ω为 ＩＲ２中的一个凸多边形区域,定义为这里的ｇ＞０为分片线性连续函数．从物理背景来看,问题（１．１）来源于轴对称共振结构中的电磁场研究．Ｍａｒｉｎｉ,Ｐｉｅｔｒａ（１９９５）［４］研究了问题（１．１）的混合有限元逼近,并得到了最优误差估计． 此文,我们采用一种新的混合元,即最小二乘混合元方法［５］;对退化问题（１．１）进行逼近,利用插值投影证明了近似解具有最优阶精度的收敛性．比较起经典混合元方法来,最小二乘混合元方法有两个优越性：有限元空间不必满足Ｌ…     

α-混合误差异方差部分线性EV模型的小波估计的Berry-Esseen界（英文）

本文使用小波估计和最小二乘的方法研究误差为α-混合异方差的部分线性EV模型,给出了参数和非参数部分的小波估计.在一般的条件下得到了小波估计量的Berry-Esseen界.     

一类Stokes方程的最小二乘混合元方法

对定常和非定常两种类型的Stokes方程建立了一类新的最小二乘混合元方法,并进行了分析,对定常的方程,采用了对u和σ的不同指标的有限元空间进行计算(LBB条件不需要),得到了最优的H1和L2模估计.对非定常的方程,采用了传统的Raviart-Thomas混合元空间,得到了最优的L2模估计.     

基于概率分布对巴音郭楞蒙古自治州风速特征的研究

基于新疆巴音郭楞蒙古自治州风速数据,讨论了分布参数估计方法和分布模型选择准则,发现混合威布尔分布是一个非常灵活的分布.采用极大似然方法和最小二乘方法,并运用四种优化算法找到参数最优估计值.同时,使用8种测度指标多重判断分布的适用性.对于混合威布尔分布,采用最小二乘法估计模型参数时,得到的分布能较好地拟合该地区风速.结果对相关部门实际分析巴音郭楞蒙古自治州风速特征和风能潜力具有参考价值.     

半导体器件瞬态模拟的对称正定混合元方法

提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题。提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定失窃工格式求解电场位势和电场强度方程;提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程,浓度函数和流函数被同时求解;采用标准的有限元方法求解热传导方程。建立了误差分析理论。     

Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems

Some least-squares mixed finite element methods for convection-diffusion problems, steady or nonstationary, are formulated, and convergence of these schemes is analyzed. The main results are that a new optimal a priori error estimate of a least-squares mixed finite element method for a steady convection-diffusion problem is developed and that four fully-discrete least-squares mixed finite element schemes for an initial-boundary value problem of a nonlinear nonstationary convection-diffusion equation are formulated. Also, some systematic theories on convergence of these schemes are established.

     

Analysis of a non-standard mixed finite element method with applications to superconvergence

We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent. Superconvergence of the latter was earlier investigated by Brandts, Chen and Yang between 2004 and 2006. Since the new method leads to a non-symmetric system matrix, its application seems however more expensive than applying the least-squares mixed finite element method. Dedicated to Ivan Hlaváček on the occasion of his 75th birthday     

SUPERCONVERGENCE OF LEAST-SQUARES MIXED FINITE ELEMENTS FOR ELLIPTIC PROBLEMS ON TRIANGULATION

In this paper, we present the least-squares mixed finite element method and investigate superconvergence phenomena for the second order elliptic boundary-value problems over triangulations. On the basis of the L~2-projection and some mixed finite element projections, we obtain the superconvergence result of least-squares mixed finite     

A Weighted Least-Squares Mixed Finite Element Formulation for Quasi-Incompressible Elastodynamics

The purpose of this work is the application of the least-squares finite element method to an elastodynamic, quasi-incompressible problem under small strain assumptions. Therefore a mixed finite element based on a weighted least-squares formulation is developed. The L₂-norm minimization of the time-discretized residuals of the given first-order system of partial differential equations leads to a functional depending on displacements and stresses. In the numerical example the proposed mixed element is compared to an alternative approach, which is based on a least-squares mixed finite element with improved momentum balance, see [1]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the use of physical spline finite element method for acoustic scattering

This paper presents the comparison of physical spline finite element method (PSFEM), in which differential equations are incorporated into interpolations of basic elements, with least-squares finite element method (LSFEM) and mixed Galerkin finite element method (MGFEM) on the numerical solution of one dimensional Helmholtz equation applied to an acoustic scattering problem. Firstly, all three methods are explained in detail and then it is shown that PSFEM reaches higher precision in a shorter time with fewer nodes than the other methods. It is also observed that this method is well suited for high frequency acoustic problems. Consequently, the results of PSFEM point out better efficiency in terms of number of unknowns and accuracy level.     

LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

1. IntroductionA large number of physical phenomena are modeled by partial differelltial equations orsystems of parabolic type in an evolutionary or eIliptic type at steady state. It is frequentlythe case that a good approximation of some function of the …     

An adaptive LSMFE method for Burgers equations

An adaptive least-squares mixed finite element method for Burgers equations is proposed and analyzed. A posteriori error estimates are obtained that are used to adaptively improve the algorithm. The least-squares functional is locally computed and is used as an effectively calculated a posteriori error estimate. The article is published in the original.     

不可压混流驱动问题的最小二乘混合元方法

1引言考虑多孔介质中两相不可压缩可混溶渗流驱动问题,它是由一组非线性耦合的椭园型压力方程和抛物型浓度方程组成：dVV。—一山人V什）gVV却）一q,VEn,（．1）＆,,。＿．、。。—一。x）＿＋u·grade－dlv（D（u）grade）一（1－c）q－,xEn,tEJ,（1．2）＆”－－’”””‘”－”””——－’——,、—’一其中a（）一a（x,c）一是（x）／卢（c）,J一［0,Ti,DcyR‘为水平油藏区域．方程式（1．l）一（1．2）中各物理量的意义如下：广为流体压力,c为流体的浓度,u为流体的Darer速度,叶为源汇项,／一—。x（q,O）,…     

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM

1. IntroductionThere are many work to investigate the stability of the mired finite element methodfor the saddle-point problems, i.e., to construct the finite element spaces, such that theso-called discrete BB-codition is satisfied (c.f. [1],[21,[7],[81 and the references therein).To circumvent the discrete BB-conditon, recently there has been an increased interest inuse of least-squares approach for the solution of the mixed finite element approximationof the saddel-point problem (c.f.[3]--[…