Abstract
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 time domain and the Galerkin finite element approach is utilized in spatial domain. The priori error estimate is derived in detail. Numerical examples are presented which are inline with the theoretical convergence rate.
Highlights
Chemistry are successfully described by the Langevin equation, which has been introduced almost 100 years before
For some particular cases, say diffusion, the original Langevin equation can be transformed into the Fokker-Planck equation
Sun et al 2 discussed the fractional model for anomalous diffusion
Summary
Chemistry are successfully described by the Langevin equation, which has been introduced almost 100 years before. Metzler et al 3 and Dubkov and Spagnolo 4 derived the fractional Fokker-Planck equation from different anomalous diffusion procedures. We mainly study the model described by the following fractional Fokker-Planck equation, which is a special case in 12 :. The discontinuous Galerkin finite element method is a very attractive method for partial differential equations because of its flexibility and efficiency in terms of mesh and shape functions. The higher order of convergence can be achieved without over many iterations Such a method was first proposed and analyzed in the early 1970s as a technique to seek numerical solutions of partial differential equations.
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