Special SIAM Student/Postdoc Seminar
In this talk, I will discuss the generalized finite element method (GFEM) for solving second order elliptic equations with heterogeneous coefficients. Optimal local approximation spaces for the GFEM constructed by the eigenfunctions of local eigenvalue problems involving partition of unity functions are presented. A nearly exponential decay rate of the local approximation errors with respect to the dimension of the local spaces at the continuous and discrete levels are established. An efficient and accurate method based on mixed formulation is proposed to solve the discrete eigenvalue problems.