共查询到19条相似文献,搜索用时 78 毫秒
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该文针对一类非线性双曲型方程提出了扩展混合有限元方法.首先,建立了半离散扩展混合元格式,获得了半离散扩展混合元解的L∞(L2)先验误差估计.然后,利用有限差分法对时间项进行离散,建立了全离散扩展混合元格式,并给出了全离散格式下的先验误差估计.最后,通过数值算例验证了理论结果. 相似文献
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首先给出二维非饱和土壤水流问题基于Crank-Nicolson(CN)方法的具有时间二阶精度的半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出误差估计,最后用数值例子说明全离散化CN有限元格式的优越性.这种方法可以绕开关于空间变量的半离散化格式的讨论,提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率. 相似文献
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《数学的实践与认识》2015,(9)
首先给出二维土壤溶质输运问题时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出CN有限元解的误差分析,最后用数值例子验证全离散化CN有限元格式的优越性.这种方法提高了时间离散的精度,并极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且方法绕开对空间变量半离散化有限元格式的讨论,使得理论研究更简便. 相似文献
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首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便. 相似文献
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周艳杰 《数学的实践与认识》2008,38(15)
在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质. 相似文献
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Burgers方程的混合元分析及其数值模拟 总被引:9,自引:0,他引:9
1.引言混合有限元法在高阶偏微分方程和含有两个战者两个以上)的未知国数的偏微分方程的数值解的研究中起着重要的作用.但是,到目前为止,混合有限元法主要是用于2n阶或一阶偏微分方程(组),如二阶椭圆型方程、平面弹性力学方程、双调和方程、Stokes和Navier-stokes方程、抛物型方程以及电磁场方程修见>到以及当中的参考文献).然而,R前混合有限元法还没有被用于对非线性的Burgers方程作数值研究.而过去对Burgers方程的数值研究主要采用标准有限元法、差分方法和谱方法修见【IO-12]以及当中的参考文献).本文的目的是用混… 相似文献
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1.引言本文的工作主要是讨论非定常的热传导一对流问题的向后一步的Euler全离散化的非线性Galerkin混合元解的存在性及其误差估计.该工作是对山中的同一问题研究的第二部分.在第一部分[1],我们已经讨论了此问题的半离散化的情形.由于所研究的目标都是非定常的热传导一对流问题,其背景是相同的,在此将不重复了,请参考[1].本文的安排如下,52先回顾非定常的热传导一对流问题的混合元解的经典性质.53回顾半离散化的非线性Galerkin混合元解的性质,并导出后续讨论需要的一些关于时间导数的估计.54讨论向后一步的Euler全离散化… 相似文献
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In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity, defined respectively on a coarse grid with grids size H and another fine grid with grid size h<< H, a finite element space Mh for the approximation of the pressure and two finite element spaces AH and Wh, for the approximation of the temperature,also defined respectivply on the coarse grid with grid size H and another fine grid with grid size h. The existence and the convergence of the fully discrete mixed element solution are shown. The scheme consists in using standard backward one step Euler-Galerkin fully discrete format at first L0 steps (L0 2) on fine grid with grid size h, but using nonlinear Galerkin mixed element method of backward one step Euler-Galerkin fully discrete format through L0 + 1 step to end step. We have proved that the fully discrete nonlinear Galerkin mixed element procedure with respect to the coarse grid spaces with grid size H holds superconvergence. 相似文献
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An H1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition. 相似文献
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This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations.The proposed method is based on the mixed finite element method in space and a finite difference scheme in time.The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail.Furthermore,We give the convergence analysis for both semidiscrete and flly discrete schemes and then prove that the numerical solution converges the exact one with order O(h2+k),where h and k:respectively denote the space step size and the time step size.Finally,numerical examples are presented to demonstrate the effectiveness of our numerical methods. 相似文献
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In this paper a mixed finite element (MFE) formulation is proposed for the initial-boundary value problem of dissipative symmetric regularized long wave (SRLW) equations with damping. Existence and uniqueness of its generalized solution and of the fully discrete mixed finite element solution are proved. Error estimates based on energy methods are given. Numerical experiments verify the theoretical analysis. 相似文献
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阻尼Sine-Gordon方程的H1-Galerkin混合元方法数值解 总被引:1,自引:0,他引:1
利用H1-Galerkin混合有限元方法讨论阻尼Sine-Gordon方程,得到一维情况下半离散和全离散格式的最优阶误差估计,并且推广应用到二维和三维情况,而且不用验证LBB相容性条件. 相似文献
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Yanping Chen Lingli Liu Zuliang Lu 《Numerical Functional Analysis & Optimization》2013,34(10):1135-1157
In this article, we shall give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results. 相似文献
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Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model 下载免费PDF全文
In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme. 相似文献