Analysis of the heterogeneous multiscale method for parabolic homogenization problems

The heterogeneous multiscale method (HMM) is applied to various parabolic problems with multiscale coefficients. These problems can be either linear or nonlinear. Optimal estimates are proved for the error between the HMM solution and the homogenized solution.

     

Optimal $\mathcal{L}^2$ error bounds for MITC3 type element

Summary. In this paper, we derive the optimal error bounds for the stabilized MITC3 element [3], the MIN3 type element [7] and the T3BL element [8]. In this way we have solved the problem proposed recently in [5] in a positive manner. Moreover, we estimate the difference between stabilized MITC3 and MIN3 and show it is of order uniform in the plate thickness. Received May 31, 2000 / Revised version received April 2, 2001 / Published online September 19, 2001     

QUADRILATERAL MESH

IntroductionQuadrilateral mesh Is widely used In the finite eleme     

A finite element method for nearly incompressible elasticity problems

A finite element method is considered for dealing with nearly incompressible material. In the case of large deformations the nonlinear character of the volumetric contribution has to be taken into account. The proposed mixed method avoids volumetric locking also in this case and is robust for (with being the well-known Lamé constant). Error estimates for the -norm are crucial in the control of the nonlinear terms.

     

Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems

We study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature. We prove, under certain sharp stability conditions, that the correct nonlinear elasticity model is given by the classical Cauchy–Born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the Cauchy–Born rule. The analysis is carried out for both simple and complex lattices, and for this purpose, we develop the necessary tools for performing asymptotic analysis on such lattices. Our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids.     

THE QUADRATIC SPECHT TRIANGLE

We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending element.The convergence result is proved under minimal smoothness assumption on the solution.Numerical results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.     

信用违约联结票券的定价

本文从定义信用违约联结票券出发,介绍了JarrowandTurnbul(1995)违约强度模型。然后在该模型的基础上,针对不同的公司,假设违约时间独立同服从指数分布且与利率期间结构独立,分别就t=0与0     

经济增长的随机AK模型

本文以经济增长AK模型(模型Ⅰ)作为基本模型,将人口数量作为不确定性的来源,建立了经济增长的随机AK模型(模型Ⅱ).分析了模型Ⅱ解的存在唯一性和M arkov性,探讨了模型Ⅱ的零均衡解的稳定性及资本-劳动比率的动态性质.     

NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.