解两点边值问题的一类修改的三次有限体积元法

构造了求解两点边值问题的一类修改的Lagrange型三次有限体积元法.试探函数空间取以四次Lobatto多项式的零点作为插值节点的Lagrange型三次有限元空间.将插值多项式的导数超收敛点(应力佳点)作为对偶单元的节点,检验函数空间取相应于对偶剖分的分片常数函数空间.证明了新方法具有最优的H1模和L2模收敛阶,讨论了在应力佳点导数的超收敛性,并通过数值实验验证了理论分析结果.     

Lagrange四边形单位分解有限元法的最优误差分析

用构造最优局部逼近空间的方法对Lagrange型四边形单位分解有限元法进行了最优误差分析.单位分解取Lagrange型四边形上的标准双线性基函数,构造了一个特殊的局部多项式逼近空间,给出了具有2阶再生性的Lagrange型四边形单位分解有限元插值格式,从而得到了高于局部逼近阶的最优插值误差.     

基于几何非协调分解的Lagrange乘子区域分解方法

本文考虑将Lagrange乘子区域分解方法应用于几何非协调分解的情况来求解二阶椭圆问题.由于采用几何非协调区域分解,每个局部乘子空间关联到多个界面,我们按照一定的规则选取合适的乘子面来定义乘子空间.利用局部正则化技巧,可以消去内部变量,得到关于Lagrange乘子的界面方程.采用一种经济的预条件迭代方法求解界面方程,且相关的预条件子是可扩展的.     

钱氏定理在有限变形极矩弹性力学广义变分原理的应用

应用Lagrange乘子法和钱伟长证明的两类广义变分原理的等价定理,在本文中导出有限变形极矩弹性力学的广义变分原理.文中采用了在拖带坐标系描述法建立的有限变形应变张量(称为Biot有限变形应变定义的准确形式)和应变速率定义与拖带系应力张量构成完整的数学描述.     

Lagrange非结构网格高阶交错型守恒气体动力学格式

提出Lagrange(拉格朗日)非结构网格高阶交错型守恒气体动力学格式.用产生于当前时刻子网格密度和网格声速的子网格压力和MUSCL方法构造了高阶子网格力,利用高阶子网格力构造了高阶空间通量,借助时间中点通量的Taylor(泰勒)展开完成了高阶时间通量离散.研制了Lagrange非结构网格高阶交错型守恒气体动力学格式.对Saltzman活塞问题等进行了数值模拟,数值结果显示了Lagrange非结构网格高阶交错型守恒气体动力学格式的有效性和精确性.     

局部域上的函数空间

研究定义在局部域上的函数空间, 包括 Triebel B型与$F$型空间,Hölder型空间, Sobolev 型空间等, 并研究定义在局部域上函数的p型导数与Hölder型空间的关系. 所获得的结果表明, 定义在Euclid空间上与定义在局部域上的函数有迥然不同的性质, 并且后者的许多结果都给出解决分形分析中重要课题的新思路与新途径.     

Lagrange函数的的两个应用

介绍Lagrange函数在大学数学教学中的两个重要应用,利用Lagrange函数中对偶问题来引入特征值和特征向量的定义,以及在规划中由已知原问题求对偶问题.     

Lagrange中值定理在线性赋范空间中推广的一个初等证明

本文将古典微积分中的Lagrange中值定理用初等的方法推广到线性赋范空间,为此,引进有关定义与引理,然后给出线性赋范空间中的微分中值定理及其推论。     

辐射流体力学Lagrange方程组一类人为解构造方法

针对一维Lagrange辐射流体力学方程组,基于物理量在Euler空间和Lagrange空间的微分关系,提出了一种人为解构造方法,并构造了一类一维Lagrange辐射流体力学方程组人为解.构造的人为解在整个计算区域光滑可微,质量方程无源项.将构造的人为解应用至二维辐射流体力学Lagrange程序中,从数值误差、收敛阶方面验证了程序的正确性,展示了人为解的可行性和适用性.     

热传导型半导体器件的二次元特征有限体积元方法及分析：H^1模估计

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.     

Longtime existence of the Lagrangian mean curvature flow

Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform -bounds in space and C²-estimates in time for the underlying Monge-Ampére equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.Received: 3 September 2002, Accepted: 12 June 2003, Published online: 4 September 2003Mathematics Subject Classification (2000): 53C44     

Lagrangian Curves in a 4-Dimensional Affine Symplectic Space

Lagrangian curves in \(\mathbb {R}^{4}\) entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in \(\mathbb {R}^{4}\) and determine Lagrangian geodesics.     

Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows

Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual Lagrangian. We give here two applications for these remarkable permanence properties. In the first, we establish for certain convex–concave Hamiltonians on a–possibly infinite dimensional–symplectic space H ², the existence of a solution for the Hamiltonian system that connects in a given time T > 0, two Lagrangian submanifolds. Another application deals with the construction of multiparameter flows, including those generated by vector fields that represent superpositions of skew-adjoint operators with gradients of convex potentials. Our methods are based on the new variational calculus for anti-selfdual Lagrangians developed in [5–7].     

Lagrangian isotopy of tori in $${S^2\times S^2}$$ and $${{\mathbb{C}}P^2}$$CP2

We show that, up to Lagrangian isotopy, there is a unique Lagrangian torus inside each of the following uniruled symplectic four-manifolds: the symplectic vector space \({{\mathbb{R}}^4}\), the projective plane \({{\mathbb{C}}P^2}\), and the monotone \({S^2 \times S^2}\). The result is proven by studying pseudoholomorphic foliations while performing the splitting construction from symplectic field theory along the Lagrangian torus. A number of other related results are also shown. Notably, the nearby Lagrangian conjecture is established for \({T^*{\mathbb{T}}^2}\), i.e. it is shown that every closed exact Lagrangian submanifold in this cotangent bundle is Hamiltonian isotopic to the zero-section.     

Biminimal Lagrangian H-umbilical submanifolds in complex space forms

All biminimal Lagrangian surfaces of nonzero constant mean curvature in 2-dimensional complex space forms have been determined in Sasahara (Differ Geom Appl 27:647?C652, 2009). In this paper, we completely determine biminimal Lagrangian H-umbilical submanifolds of nonzero constant mean curvature in complex space forms of dimension ?? 3.     

Willmore Lagrangian Spheres in the Complex Euclidean Space C n

In this paper we construct many examples of n-dimensionalWillmore Lagrangian submanifolds in the complex Euclidean space C ⁿ . We characterize them as the only Willmore Lagrangian submanifolds invariant under the action of SO(n). The mostimportant contribution of our construction is that it provides examplesof Willmore Lagrangian spheres in C ⁿ for all n 2.     

Ruled Special Lagrangian 3-Folds In C3

This is the fifth in a series of papers constructing explicitexamples of special Lagrangian submanifolds in C^m. A submanifoldof C^m is ruled if it is fibred by a family of real straightlines in C^m. This paper studies ruled special Lagrangian 3-foldsin C³, giving both general theory and families of examples.Our results are related to previous work of Harvey and Lawson,Borisenko, and Bryant. Special Lagrangian cones in C³ are automaticallyruled, and each ruled special Lagrangian 3-fold is asymptoticto a unique special Lagrangian cone. We study the family ofruled special Lagrangian 3-folds N asymptotic to a fixed specialLagrangian cone N0. We find that this depends on solving a linearequation, so that the family of such N has the structure ofa vector space. We also show that the intersection of N0 withthe unit sphere S⁵ in C³ is a Riemann surface, and constructa ruled special Lagrangian 3-fold N asymptotic to N0 for eachholomorphic vector field w on . As corollaries of this we writedown two large families of explicit special Lagrangian 3-foldsin C³ depending on a holomorphic function on C, which includemany new examples of singularities of special Lagrangian 3-folds.We also show that each special Lagrangian T2-cone N0 can beextended to a 2-parameter family of ruled special Lagrangian3-folds asymptotic to N0, and diffeomorphic to T²xR. 2000 Mathematical Subject Classification: 53C38, 53D12.     

On base manifolds of Lagrangian fibrations

We consider base spaces of Lagrangian fibrations from singular symplectic varieties.After defining cohomologically irreducible symplectic varieties,we construct an example of Lagrangian fibration whose base space is isomorphic to a quotient of the projective space.We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.     

An example of special lagrangian fibration

On the total space of the line bundle π:π1*T*P1(?)π2*T*P1→P1×P1,a complete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given. This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4 directions.     

Convergence Rate of the Augmented Lagrangian SQP Method

In this paper, the augmented Lagrangian SQP method is considered for the numerical solution of optimization problems with equality constraints. The problem is formulated in a Hilbert space setting. Since the augmented Lagrangian SQP method is a type of Newton method for the nonlinear system of necessary optimality conditions, it is conceivable that q-quadratic convergence can be shown to hold locally in the pair (x, ). Our interest lies in the convergence of the variable x alone. We improve convergence estimates for the Newton multiplier update which does not satisfy the same convergence properties in x as for example the least-square multiplier update. We discuss these updates in the context of parameter identification problems. Furthermore, we extend the convergence results to inexact augmented Lagrangian methods. Numerical results for a control problem are also presented.