A note on the finite element method for the space-fractional advection diffusion equation

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Abstract

In this paper, a note on the finite element method for the space-fractional advection diffusion equation with non-homogeneous initial-boundary condition is given, where the fractional derivative is in the sense of Caputo. The error estimate is derived, and the numerical results presented support the theoretical results.

Keywords

Space-fractional partial differential equation
Caputo derivative
Finite element method

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This work was partially supported by the Natural Science Foundation of China under grant no. 10872119, Shanghai Leading Academic Discipline Project under grant no. S30104. and Huainan Normal University under grant no. 2007LKQ07.