Finite element multigrid method for multi-term time fractional advection diffusion equations

In this paper, a class of multi-term time fractional advection diffusion equations (MTFADEs) is considered. By finite difference method in temporal direction and finite element method in spatial direction, two fully discrete schemes of MTFADEs with different definitions on multi-term time fractional derivative are obtained. The stability and convergence of these numerical schemes are discussed. Next, a V-cycle multigrid method is proposed to solve the resulting linear systems. The convergence of the multigrid method is investigated. Finally, some numerical examples are given for verification of our theoretical analysis.