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

Xin Fei Liu | Zendy; Yang Liu | Zendy; Hong Li | Zendy; Zhi Chao Fang | Zendy; Jinfeng Wang | Zendy

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

Author(s) -

Xin Fei Liu,

Yang Liu,

Hong Li,

Zhi Chao Fang,

Jinfeng Wang

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.229

Subject(s) - mathematics , stability (learning theory) , convergence (economics) , convection–diffusion equation , order (exchange) , diffusion equation , finite element method , approximation error , mathematical analysis , time derivative , fractional calculus , rate of convergence , diffusion , physics , computer science , thermodynamics , computer network , channel (broadcasting) , economy , finance , service (business) , machine learning , economics , economic growth

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 + τ3−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.

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