共查询到19条相似文献,搜索用时 124 毫秒
1.
2.
非线性对流扩散方程沿特征线的多步有限体积元格式 总被引:4,自引:1,他引:3
对于二维非线性对流扩散方程构造了沿特征线方向的多步有限体积元格式.关于空间采用二次有限体积元方法离散,关于时间采用多步法进行离散,获得了O(Δt^2 h^2)形式的误差估计.本文最后给出的数值算例表明了方法的有效性. 相似文献
3.
将特征线方法与有限体积元方法相结合,采用分片线性函数和分片常数函数分别作为有限体积元方法的试探函数和检验函数空间,构造了热传导型半导体器件的全离散特征有限体积元格式.并进行收敛性分析,在一般的条件下得到了最优阶H1模误差估计结果. 相似文献
4.
陈传军 《高等学校计算数学学报》2005,27(3):279-288
1、引言 有限体积元方法作为求解微分方程的一种新技术,日益受到普遍关注.本文将特征线方法与有限体积元方法相结合,构造出特征有限体积元方法,该方法综合了特征有限差分方法和特征有限元方法的主要优点,与特征有限差分方法相比, 相似文献
5.
该文构造了热传导型半导体器件的全离散特征有限体积元格式,将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间,并进行误差分析,得到了最优阶 H1模误差估计结果. 相似文献
6.
该文构造了热传导型半导体器件的全离散特征有限体积元格式,将特征线方法与有限体积元方法相结合, 采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间,并进行误差分析,得到了最优阶H1模误差估计结果. 相似文献
7.
二维热传导型半导体瞬态问题的二次元特征有限体积元方法 总被引:1,自引:0,他引:1
陈传军 《高校应用数学学报(A辑)》2005,20(2):185-196
将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间构造了二维热传导型半导体瞬态问题的全离散二次元特征有限体积元格式,并进行误差分析,得到了次优阶L^2模误差估计结果. 相似文献
8.
9.
将时间间断的时空元思想与基于等距节点下三次Lagrange插值的超收敛有限体积元方法相结合,以三次Lagrange插值导数超收敛点为对偶剖分节点,引入插值投影算子,建立对流扩散方程的时间间断时空有限体积元格式.结合有限体积元分析与以Radau积分点为节点的Lagrange插值,证明了近似解的最优L∞(L2)-模误差估计... 相似文献
10.
半导体器件的瞬时状态由包含3个拟线性偏微分方程所组成的方程组的初边值问题来描述.在三角剖分的基础上,对椭圆型的电子位势方程采用混合有限体积元法来逼近,对对流扩散型的电子浓度和空穴浓度方程采用迎风有限体积元方法来逼近,并进行了详细的理论分析,得到了最优阶的误差估计结果.最后,针对混合有限体积元法和迎风有限体积元法分别单独使用以及两种方法结合使用的情形给出了不同的数值算例. 相似文献
11.
本文利用基于重心对偶剖分的有限体积元法建立了二维非饱和土壤水分运动问题的数值逼近格式,讨论了离散有限体积元解的存在唯一性,并给出了最优误差估计的证明.最后给出数值算例,模拟结果表明,利用有限体积元格式来求解二维非饱和土壤水分运动问题是可靠的,且该格式具有稳定性和可实用性. 相似文献
12.
Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an appropriate, critical quadrature rule; this allows the elimination of the flux and Lagrange multiplier parameters so as to obtain equations in the scalar variable, which will define the finite volume method. Following this derivation with different mixed finite element spaces leads to a variety of finite volume schemes. In particular, we restrict ourselves to finite volume methods posed over rectangular partitions and begin by studying an efficient second-order finite volume method based on the Brezzi–Douglas–Fortin–Marini space of index two. Then, we present a general global analysis of the difference between the solution of the underlying mixed finite element method and its related finite volume method. Then, we derive finite volume methods of all orders from the Raviart–Thomas two-dimensional rectangular elements; we also find finite volume methods to associate with BDFM
2 three-dimensional rectangles. In each case, we obtain optimal error estimates for both the scalar variable and the recovered flux. 相似文献
13.
对流扩散方程的有限体积-有限元方法的误差估计 总被引:5,自引:1,他引:4
本文结合有限体积方法和有限元方法处理非线性对流扩散问题,非线性对流项利用有限体积方法处理,扩散项利用有限元方法离散,并给近似解的误差估计。 相似文献
14.
In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence
of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between
the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing
projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization
is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries.
Finally, some numerical experiments that confirm the predicted behavior of the method are provided. 相似文献
15.
《Journal of Computational and Applied Mathematics》2002,146(2):373-386
The finite volume element method is a discretization technique for partial differential equations, but in general case the coefficient matrix of its linear system is not symmetric, even for the self-adjoint continuous problem. In this paper we develop a kind of symmetric modified finite volume element methods both for general self-adjoint elliptic and for parabolic problems on general discretization, their coefficient matrix are symmetric. We give the optimal order energy norm error estimates. We also prove that the difference between the solutions of the finite volume element method and symmetric modified finite volume element method is a high order term. 相似文献
16.
Chunjia Bi 《Numerical Methods for Partial Differential Equations》2007,23(1):220-233
In this article, we consider the finite volume element method for the second‐order nonlinear elliptic problem and obtain the H1 and W1,∞ superconvergence estimates between the solution of the finite volume element method and that of the finite element method, which reveal that the finite volume element method is in close relationship with the finite element method. With these superconvergence estimates, we establish the Lp and W1,p (2 < p ≤ ∞) error estimates for the finite volume element method for the second‐order nonlinear elliptic problem. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
17.
The object of this paper is to complete the results obtained in [3] by showing that the new mixed finite element that we have
constructed in [3] also works for quadrilateral elements and to compare this method with the standard finite volume method.
Estimates of optimal order are derived for both the new mixed finite element and an associated finite volume method. 相似文献
18.
The object of this paper is to complete the results obtained in [3] by showing that the new mixed finite element that we have constructed in [3] also works for quadrilateral elements and to compare this method with the standard finite volume method. Estimates of optimal order are derived for both the new mixed finite element and an associated finite volume method. 相似文献
19.
Chunjia Bi 《高等学校计算数学学报(英文版)》2006,15(1):82-96
In this paper,we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems. It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H~1-and L~2-norms. 相似文献