Finite element multigrid method for the boundary value problem of fractional advection dispersion equation

The stationary fractional advection dispersion equation is discretized by linear finite element scheme,and a full v-cycle multigrid method (fv-mgm) is proposed to solve the resulting system. some useful properties of the approximation and smoothing operators are proved. using these properties we derive the convergence results in both l 2 norm and energy norm for fv-mgm. numerical examples are given to demonstrate the convergence rate and efficiency of the method. © 2013 zhiqiang zhou and hongying wu.