Finite Element Multigrid Method for the Boundary Value Problem of Fractional Advection Dispersion Equation

Abstract

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 norm and energy norm for FV-MGM. Numerical examples are given to demonstrate the convergence rate and efficiency of the method.