| Volume 8, Number 1, 2018, Pages 229-249 DOI：10.11948/2018.229 |
| Finite element algorithm based on high-order time approximation for time fractional convection-diffusion equation |
| Xinfei Liu,Yang Liu,Hong Li,Zhichao Fang,Jinfeng Wang |
| Keywords:Time fractional convection-diffusion equation, high-order approximation, finite element method, error estimates. |
| Abstract: |
| In this paper, finite element method with high-order approximation for time fractional derivative is considered and discussed to find the numerical solution of time fractional convection-diffusion equation. Some lemmas are introduced and proved, further the stability and error estimates are discussed and analyzed, respectively. The convergence result $O(h^{r+1}+\tau^{3-\alpha})$ can be derived, which illustrates that time convergence rate is higher than the order $(2-\alpha)$ derived by $L1$-approximation. Finally, to validate our theoretical results, some computing data are provided. |
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