| Issue |
ESAIM: M2AN
Volume 54, Number 6, November-December 2020
|
|
|---|---|---|
| Page(s) | 2265 - 2294 | |
| DOI | https://doi.org/10.1051/m2an/2020018 | |
| Published online | 11 November 2020 | |
Numerical algorithm for the model describing anomalous diffusion in expanding media
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
* Corresponding author: dengwh@lzu.edu.cn
Received:
12
October
2019
Accepted:
11
March
2020
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in Le Vot et al. [Phys. Rev. E 96 (2017) 032117]. The Sobolev regularity for the equation with variable coefficient is first established. Then we use the finite element method to discretize the Laplace operator and present error estimate of the spatial semi-discrete scheme based on the regularity of the solution; the backward Euler convolution quadrature is developed to approximate Riemann–Liouville fractional derivative and the error estimates for the fully discrete scheme are established by using the continuity of solution. Finally, the numerical experiments verify the effectiveness of the algorithm.
Mathematics Subject Classification: 65M60 / 42A85 / 35R11
Key words: Fractional diffusion equation / variable coefficient / finite element method / convolution quadrature / error analysis
© EDP Sciences, SMAI 2020
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