Jin, B;
Yan, Y;
Zhou, Z;
(2019)
Numerical approximation of stochastic time-fractional diffusion.
ESAIM: Mathematical Modelling and Numerical Analysis
, 53
(4)
pp. 1245-1265.
10.1051/m2an/2019025.
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Abstract
We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order α ∈ (0, 1), and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order γ ∈ [0, 1] in the front). The numerical scheme approximates the model in space by the standard Galerkin method with continuous piecewise linear finite elements and in time by the classical Gr¨unwald-Letnikov method (for both Caputo fractional derivative and Riemann-Liouville fractional integral), and the noise by the L 2 -projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the discrete solution operators for the deterministic inhomogeneous problem. One- and two-dimensional numerical results are presented to support the theoretical findings.
| Type: | Article |
|---|---|
| Title: | Numerical approximation of stochastic time-fractional diffusion |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an/2019025 |
| Publisher version: | https://doi.org/10.1051/m2an/2019025 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10070473 |
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