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

Published online by Cambridge University Press:  03 June 2015

Na Zhang ,
Weihua Deng  and
Yujiang Wu
Na Zhang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Weihua Deng*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Yujiang Wu*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
*
Email: [email protected]
Corresponding author. Email: [email protected]
Email: [email protected]
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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.

Keywords

26A3365M0665M1265M60Modified subdiffusion equationfinite difference methodfinite element methodstabilityconvergence rate
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 4 , August 2012 , pp. 496 - 518
Copyright
Copyright © Global-Science Press 2012

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