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Copyright © 2012 Y. J. Choi and S. K. Chung. Y. J. Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+[superscript]hγ [/superscript] ) , where γ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.

Details

Title
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Author
Choi, Y J; Chung, S K
Publication year
2012
Publication date
2012
Publisher
John Wiley & Sons, Inc.
ISSN
10853375
e-ISSN
16870409
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1040682975
Copyright
Copyright © 2012 Y. J. Choi and S. K. Chung. Y. J. Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.