On the Finite Element Method for the Time-Space Fractional Advection Dispersion Equation
In this paper, we study the time-space fractional order (fractional for simplicity) advection dispersion equation, which can be an application as a model for anomalous diffusion or fractional diffusion. The fully discrete numerical approximation is analyzed where the Galerkin finite element method for the space Riemann-Liouville fractional derivative with order 1+β∈1, 2) and the finite difference scheme for the time Caputo derivative with order α∈(0, 1). Results on variational solution of the error estimates are presented. Numerical examples are included to confirm the theoretical estimates.
Time-space fractional advection dispersion equation Riemann-Liouville derivative Caputo derivative difference method finite element method.
Changpin Li Zhengang Zhao
Department of Mathematics, Shanghai University, Shanghai 200444, China.
国际会议
青岛
英文
458-463
2010-07-15（万方平台首次上网日期，不代表论文的发表时间）