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

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  • Yunying Zheng
  • Zhengang Zhao

Abstract

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.

Suggested Citation

  • Yunying Zheng & Zhengang Zhao, 2011. "A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-20, October.
    • Handle: RePEc:hin:jnlmpe:171620
    DOI: 10.1155/2011/171620
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