A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation | Zendy

Yunying Zheng | Zendy; Zhengang Zhao | Zendy

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A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

Author(s) -

Yunying Zheng,

Zhengang Zhao

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/171620

Subject(s) - mathematics , fractional calculus , nonlinear system , mathematical analysis , diffusion equation , galerkin method , anomalous diffusion , advection , fractal , space (punctuation) , diffusion , derivative (finance) , crank–nicolson method , diffusion process , discretization , physics , computer science , knowledge management , economy , innovation diffusion , quantum mechanics , financial economics , economics , thermodynamics , service (business) , operating system

The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis

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