共查询到19条相似文献,搜索用时 78 毫秒
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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. 相似文献
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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… 相似文献
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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. 相似文献
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《数学的实践与认识》2020,(9)
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. 相似文献
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半导体器件瞬态模拟的对称正定混合元方法 总被引:3,自引:3,他引:0
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。 相似文献
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Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems 总被引:6,自引:0,他引:6
Dan-Ping Yang. 《Mathematics of Computation》2000,69(231):929-963
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.
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Jan H. Brandts 《Applications of Mathematics》2009,54(3):225-235
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 相似文献
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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 相似文献
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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) 相似文献
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Gökhan Apaydin 《Applied mathematics and computation》2010,215(10):3576-3588
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. 相似文献
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Dan-ping Yang 《计算数学(英文版)》2002,20(2):153-164
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 … 相似文献
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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. 相似文献
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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),… 相似文献
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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]--[… 相似文献