Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Keyword(s):
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 asO(k+hγ˜), whereγ˜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.
2017 ◽
Vol 25
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pp. 1601-1617
2017 ◽
Vol 25
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2014 ◽
Vol 599-601
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pp. 1305-1308
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2015 ◽
Vol 93
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pp. 1212-1225
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Vol 05
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pp. 135-157
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2019 ◽
Vol 78
(5)
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pp. 1367-1379
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