Multiscale Asymptotic Analysis For Elastic Problems Of Composite Materials And Mixed Finite Element

In this paper, we mainly discussed a kind of very important mathematics physics issue: elastic problems of composite materials with small periodic coefficient.First, with the asympototic expansion and homogenized method, a nonconforming Crouzeix-Raviart finite element is applied to estimate every item of the asympototic expansion on anisotropic meshes. At the same time, the approximation format to the higher derivative of the homogenized solution is bulit. At last, the optimal error estimate in ||·||_h is derived.Then, based on the multi-scale asympototic expansion, we discussed a mixed finite element method for the homogenized equations on anisotropic meshes and obtained the corresponding error estimate. This element has relieved the regular condition fetter, has a better use .