A novel finite element method for a class of time fractional diffusion equations

Abstract

Anomalous transport of contaminants in groundwater or porous soil is a research focus in hydrology and soil science for decades. Because fractional diffusion equations can well characterize early breakthrough and heavy tail decay features of contaminant transport process, they have been considered as promising tools to simulate anomalous transport processes in complex media. However, the efficient and accurate computation of fractional diffusion equations is a main task in their applications. In this paper, we introduce a novel numerical method which captures the critical Mittag-Leffler decay feature of subdiffusion in time direction, to solve a class of time fractional diffusion equations. A key advantage of the new method is that it overcomes the critical problem in the application of time fractional differential equations: long-time range computation. To illustrate its efficiency and simplicity, three typical academic examples are presented. Numerical results show a good agreement with the exact solutions. © 2011 by ASME.