Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations | Zendy

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

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Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

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 - 10.1155/2013/857205

Subject(s) - mathematics , discretization , uniqueness , finite element method , convergence (economics) , mathematical analysis , stability (learning theory) , partial differential equation , numerical analysis , quadrature (astronomy) , physics , computer science , machine learning , optics , economics , thermodynamics , economic growth

A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions

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