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Choi, Y. J.; Chung, S. K.

Finite element solutions for the space fractional diffusion equation with a nonlinear source term. (English) Zbl 1253.65148

Abstr. Appl. Anal. 2012, Article ID 596184, 25 p. (2012).
Summary: 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 \(O(k + h^{\tilde{\gamma}})\), where \(\tilde{\gamma}\) 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.

Cited in 12 Documents

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35K57 Reaction-diffusion equations

Keywords:

finite element Galerkin solutions; space fractional diffusion equation

Software:

FODE
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References:

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