A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain | Zendy

Jingjun Zhao | Zendy; Jingyu Xiao | Zendy; Yang Xu | Zendy

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A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain

Author(s) -

Jingjun Zhao,

Jingyu Xiao,

Yang Xu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/868035

Subject(s) - discretization , uniqueness , mathematics , finite element method , mathematical analysis , convergence (economics) , advection , quadrature (astronomy) , space (punctuation) , diffusion , physics , computer science , optics , economics , thermodynamics , economic growth , operating system

We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solution by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatialdiscretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well with the main conclusions

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