Two-scale finite element Green’s function approximations with applications to electrostatic potential computation

In this paper, a two-scale finite element approach is proposed and analyzed for approximations of Green’s function in three-dimensions. This approach is based on a two-scale finite element space defined, respectively, on the whole domain with size H and on some subdomain containing singular points with size h (h ≪ H). It is shown that this two-scale discretization approach is very efficient. In particular, the two-scale discretization approach is applied to solve Poisson-Boltzmann equations successfully.