FE-HMM For Elliptic Eigenvalue Problems With Highly Oscillatory Coefficients

The purpose of this thesis is to design multiscale methods for elliptic eigenvalue problems with highly oscillatory coefficients,based on the homogenization theory of elliptic eigenvalue problems and the heterogeneous multiscale method.The thesis can be divided into three parts.In the first part,we introduce the finite element method.In the second part,we describe the heterogeneous multiscale method.In the third part,based on the homogenization theory,we study the asymptotic behaviour of partial differential equations.For periodic coefficients,we can get the explicit homogenization equation,the solution of which is the weak limit of that of the original equation.Similarly,for elliptic eigenvalue problems,eigenpairs of the original equation converge weakly to the corresponding eigenpairs of the homogenization problem.Numerical experiments show that the FE-HMM for eigenvalue problem has same approximation error as that for boundary-value problems.