Multiscale computation method for an advection–diffusion equation

In this paper, we consider the initial-boundary value problem of the advection–diffusion equation with rapidly oscillating coefficients in both time and space domain. A multiscale asymptotic expansion of the solution for this kind of problem is presented. A full discrete finite element method for computing above mentioned problem is introduced. The proposed method not only can greatly save computer memory and CPU time, but also has high precision for approximating the solution. The numerical results show that the method presented in this paper is effective and reliable.