Leapfrog/Finite Element Method for Fractional Diffusion Equation
Keyword(s):
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove anL2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
2017 ◽
Vol 120
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pp. 270-286
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2014 ◽
Vol 05
(04)
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pp. 1450022
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2018 ◽
Vol 59
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pp. 441-463
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2021 ◽
Vol 493
(2)
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pp. 124540
Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation
2020 ◽
Vol 367
◽
pp. 112435
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2015 ◽
Vol 05
(02)
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pp. 135-157
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2020 ◽
Vol 79
(9)
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pp. 2784-2794
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