共查询到19条相似文献,搜索用时 687 毫秒
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双曲型积分-微分方程的有限体积元方法 总被引:1,自引:0,他引:1
本文研究了双曲型积分—微分方程的有限体积元方法,利用基于有限体积元的Ritz—Volterra投影的逼近性质,得到了半离散有限体积元解的最优阶L2,H^1,L∞和W^1,∞模误差估计. 相似文献
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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
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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
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《数学物理学报(A辑)》2017,(5)
该文主要研究一维非线性抛物问题两层网格有限体积元逼近.对一维非线性抛物问题有限体积元解的存在性进行了讨论,给出了最优阶L~2-模和H~1-模误差估计结果,并研究了其两层网格算法.证明了当粗细网格步长满足h=O(H~2)时两层网格算法具有最优阶H~1-模误差估计.数值算例验证了理论结果. 相似文献
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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
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本文用具有调整对流的特征线修正方法(MMOCAA)与有限体积元方法相结合,构造出一种新的守恒型计算格式-MMOCAAFVEM,这种方法综合了特征线方法和有限体积元方法的主要优点.通过对对流项进行调整,以很小的额外计算量获取了问题的质量守恒性质,并且证明该方法具有最优阶H1误差估计. 相似文献
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In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H^1 norm error estimates. A numerical example is given at the end to show the feasibility of the method. 相似文献
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Tong Zhang 《计算数学(英文版)》2013,31(5):470-487
In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O(H2) or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0(I log hll/2H3). These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods. 相似文献
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The Alternating-direction Implicit Characteristic Finite Element Methods for the Three-dimensional Generalized Nerve Conduction Equation 下载免费PDF全文
Zhiyue Zhang 《偏微分方程(英文版)》2001,14(3):207-219
A complete convergence nnalysis is given for two-level scheme of the alternating-direction implicit characteristic finite element method for the approximate solution of the three-dimensional generalized nerve conduction equation. By use of the calculation of vector product, H^{-1} norm estimates, and a priori estimate theory and technique, the optimal order estimate in L² is obtained. 相似文献
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In this paper, we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by $H^{1}$-Galerkin mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization, and backward Euler scheme for temporal discretization. Firstly, a priori error estimates and some superclose properties are derived. Secondly, a two-grid scheme is presented and its convergence is discussed. In the proposed two-grid scheme, the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal accuracy. Finally, a numerical experiment is implemented to verify theoretical results of the proposed scheme. The theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice $h=H^2$. 相似文献
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Summary. In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law with initial condition . The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution
given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and
the entropy solution. The order of these estimates is in space-time -norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the
stiff case.
Received October 21, 1999 / Published online February 5, 2001 相似文献
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A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by $H^1(\Omega)$-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of $L^2(H^1)$-norm for the velocity field, $L^2(L^2)$-norm for the pressure and the broken $L^2(H^1)$-norm for the magnetic field are derived. 相似文献
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Tongke 《高等学校计算数学学报(英文版)》2010,3(4)
<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods. 相似文献
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Weak Galerkin finite element methods combined with Crank-Nicolson scheme for parabolic interface problems 下载免费PDF全文
This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ norms are established for lowest order WG finite element space $({\cal P}_{k}(K),\;{\cal P}_{k-1}(\partial K),\;\big[{\cal P}_{k-1}(K)\big]^2)$. Finally, we give numerical examples to verify the theoretical results. 相似文献
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Yanni Gao & Yanli Chen 《数学研究通讯:英文版》2015,31(4):320-332
In this paper, a biquartic finite volume element method based on LobattoGuass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some superconvergent properties are available and could be proved for this method. The numerical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method. 相似文献