变分问题

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

In this paper, a novel method called the variational iteration method is proposed to solve perturbation problems.

本文提出了求解摄动问题的一种新方法——变分迭代算法。

We introduce the iterative method of Jacobi type to solve the discrete problem of the quasivariational inequality system. A new proof for the monotone convergence of the iterative method is given under appropriate conditions.

我们首先介绍求解Hamilton-Jacobi-Bellman方程的近似拟变分不等式组离散问题的一类Jacobi型迭代算法，在一定假设条件下，对这类算法的单调收敛性给出了一个新的证明。

The rigid-flexible coupling dynamics of flexible multibody systems with free largeoverall motions is studied for the first time in chapter 6.The equations of the motion forthe flexible multibody system are obtained utilizing Jourdain's velocity variationalprinciple and forward recursive formulation.

第六章首次对大范围运动为自由的柔性多体系统的刚-柔耦合动力学问题进行研究，用Jourdain速度变分原理和单向递推组集建模方法建立了柔性多体系统的刚-柔耦合动力学方程。

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

In our problem,the major term in the variational inequality isp-Laplacian.

在我们所考虑的问题中，变分不等式的主部是p-Laplace算子。

Variational principle is a powerful tool in many scientific aspects. It has been widely used in mathematical physics, and especially it has been successfully used in solid mechanics.

变分原理在数学物理问题中有着广泛的应用，在很多科技领域中都是一种强有力的工具，它在固体力学领域中，更是运用得卓有成效。

The form of the maximum principle is similar to its risk-neutral counterpart.

利用经典的凸变分方法，我们得到了该类问题的最大值原理。

It is a very important numerical method for solving variational inequality and complementarity problem.

它是求解变分不等式与互补问题的一类重要算法。

In this thesis, we construct and analyze some efficient numerical methods for solving variational inequality and complementarity problem.

本文讨论了求解几类变分不等式与互补问题的有效算法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。