Journal of Applied Mathematics
Volume 2013 (2013), Article ID 385463, 8 pages
http://dx.doi.org/10.1155/2013/385463
Research Article

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

Zhiqiang Zhou and Hongying Wu

Department of Mathematics, Huaihua University, Huaihua 418008, China

Received 2 March 2013; Accepted 14 May 2013

Academic Editor: Morteza Rafei

Copyright © 2013 Zhiqiang Zhou and Hongying Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.