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 $L^2$ norm and energy norm for FV-MGM. Numerical examples are given to demonstrate the convergence rate and efficiency of the method.