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A fully discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation. (English) Zbl 1202.65157

Summary: The fractional Fokker-Planck equation is often used to characterize anomalous diffusion. In this paper, a fully discrete approximation for the nonlinear spatial fractional Fokker-Planck equation is given, where the discontinuous Galerkin finite element approach is utilized in the time domain and the Galerkin finite element approach is utilized in the spatial domain. An a priori error estimate is derived explicitly. Numerical examples are presented which are in line with the theoretical convergence rate.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q84 Fokker-Planck equations
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References:

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