Numerical algorithm for the model describing anomalous diffusion in expanding media
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 2265-2294.

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.

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Accepté le :
Publié le :
DOI : 10.1051/m2an/2020018
Classification : 65M60, 42A85, 35R11
Mots-clés : Fractional diffusion equation, variable coefficient, finite element method, convolution quadrature, error analysis 
@article{M2AN_2020__54_6_2265_0,
     author = {Nie, Daxin and Sun, Jing and Deng, Weihua},
     title = {Numerical algorithm for the model describing anomalous diffusion in expanding media},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2265--2294},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {6},
     year = {2020},
     doi = {10.1051/m2an/2020018},
     mrnumber = {4173149},
     zbl = {1476.65246},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2020018/}
}
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Nie, Daxin; Sun, Jing; Deng, Weihua. Numerical algorithm for the model describing anomalous diffusion in expanding media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 2265-2294. doi : 10.1051/m2an/2020018. http://www.numdam.org/articles/10.1051/m2an/2020018/

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