FINITE ELEMENT ALGORITHM BASED ON HIGH-ORDER TIME APPROXIMATION FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION

Xin Fei Liu; Yang Liu; Hong Li; Zhi Chao Fang; Jin Feng Wang

doi:10.11948/2018.229

2018 Volume 8 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2018 > 8(1): 229-249

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Xin Fei Liu, Yang Liu, Hong Li, Zhi Chao Fang, Jin Feng Wang. FINITE ELEMENT ALGORITHM BASED ON HIGH-ORDER TIME APPROXIMATION FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 229-249. doi: 10.11948/2018.229

Citation:

Xin Fei Liu, Yang Liu, Hong Li, Zhi Chao Fang, Jin Feng Wang. FINITE ELEMENT ALGORITHM BASED ON HIGH-ORDER TIME APPROXIMATION FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 229-249. doi: 10.11948/2018.229

FINITE ELEMENT ALGORITHM BASED ON HIGH-ORDER TIME APPROXIMATION FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION

1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2 School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China

Fund Project:

Abstract

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 + τ^3-α) can be derived, which illustrates that time convergence rate is higher than the order (2-α) derived by L1-approximation. Finally, to validate our theoretical results, some computing data are provided.
- Time fractional convection-diffusion equation /
- high-order approximation /
- finite element method /
- error estimates
MSC: 65N30;65M60;26A33

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References

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