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1.
An H^1-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   

2.
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   

3.
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   

4.
四阶强阻尼波方程的新混合元方法   总被引:7,自引:3,他引:4  
刘洋  李宏 《计算数学》2010,32(2):157-170
构造半线性四阶强阻尼波动方程的新H1-Galerkin混合有限元方法,得到一维情况下半离散和全离散格式最优收敛阶误差估计,并且推广到二维和三维情况,不用验证LBB相容性条件.  相似文献   

5.
In this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the incompressible Navier–Stokes equations using a finite element approximation for the space discretization. We consider two situations. In the first one, the analysis relies on the satisfaction of the inf-sup condition for the velocity-pressure finite element spaces. After that, we study a fully discrete fractional step method using a Poisson equation for the pressure. In this case the velocity-pressure interpolations do not need to accomplish the inf-sup condition and in fact we consider the case in which equal velocity-pressure interpolation is used. Optimal convergence results in time and space have been obtained in both cases.  相似文献   

6.
双曲型积分微分方程H~1-Galerkin混合元法的误差估计   总被引:15,自引:1,他引:14  
王瑞文 《计算数学》2006,28(1):19-30
本文用H1-Galerkin混合有限元法分析了基于带有记忆项的多孔介质中的对流问题的数学模型,即双曲型积分微分方程.我们得到了在一维情况下函数和它梯度的最优阶误差估计, 并且由此推广到二维和三维情况下,得到了和用传统的混合元方法相同的收敛阶数,而且不用验证满足LBB相容性条件.  相似文献   

7.
利用稳定化方法讨论拉格朗日乘子法得到的具有弱对称应力的线弹性问题. 用线性元和分片常数分别逼近变分问题的应力和位移. 并通过添加稳定项$G_1(\cdot,\cdot)$, $G_2(\cdot,\cdot)$和$G_3(\cdot,\cdot)$ 使相应混合离散变分问题满足弱BB条件. 接着详细研究了变分问题的解与稳定混合有限元解之间的误差估计,最后用两个数值算例验证理论分析的有效性.  相似文献   

8.
利用修正的H~1-Galerkin混合有限元方法研究了广义神经传播方程,论证了其半离散解的存在唯一性,得到了半离散解的最优阶误差估计,该方法的优点是不需验证LBB相容性条件.  相似文献   

9.
In this work we consider a stabilized Lagrange (or Kuhn–Tucker) multiplier method in order to approximate the unilateral contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed in the convergence analysis. We propose three approximations of the contact conditions well adapted to this method and we study the convergence of the discrete solutions. Several numerical examples in two and three space dimensions illustrate the theoretical results and show the capabilities of the method.  相似文献   

10.
Mortar methods with dual Lagrange multiplier bases provide a flexible, efficient and optimal way to couple different discretization schemes or nonmatching triangulations. Here, we generalize the concept of dual Lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the Lagrange multiplier space have the same dimension. We provide a new theoretical framework within this relaxed setting, which opens a new and simpler way to construct dual Lagrange multiplier bases for higher order finite element spaces. As examples, we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements. Numerical results illustrate the performance of our approach. This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12, the Netherlands Organization for Scientific Research and by the European Community's Human Potential Programme under contract HPRN-CT-2002-00286.  相似文献   

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