Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 596184, 25 pages.
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
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 , where 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.
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 596184, 25 pages.
First available in Project Euclid: 5 April 2013
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Choi, Y. J.; Chung, S. K. Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 596184, 25 pages. doi:10.1155/2012/596184. https://projecteuclid.org/euclid.aaa/1365168355