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Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation

Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation
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Year:    2012

Author:    Na Zhang, Weihua Deng, Yujiang Wu

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 496–518

Abstract

We present the finite difference/element method for a two-dimensional modified fractional diffusion equation. The analysis is carried out first for the time semi-discrete scheme, and then for the full discrete scheme. The time discretization is based on the $L1$-approximation for the fractional derivative terms and the second-order backward differentiation formula for the classical first order derivative term. We use finite element method for the spatial approximation in full discrete scheme. We show that both the semi-discrete and full discrete schemes are unconditionally stable and convergent. Moreover, the optimal convergence rate is obtained. Finally, some numerical examples are tested in the case of one and two space dimensions and the numerical results confirm our theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m1210

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 496–518

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Modified subdiffusion equation finite difference method finite element method stability convergence rate.

Author Details

Na Zhang

Weihua Deng

Yujiang Wu

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