| Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
|---|---|---|
| Page(s) | 389 - 418 | |
| DOI | https://doi.org/10.1051/m2an/2024080 | |
| Published online | 08 January 2025 | |
Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise
1
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
2
State Key Laboratory of Natural Product Chemistry, Lanzhou University, Lanzhou 730000, P.R. China
* Corresponding author: dengwh@lzu.edu.cn
Received:
31
October
2022
Accepted:
6
November
2024
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters H1, … , Hd+1 ∈ (0, ½] and d = 1, 2. We first provide the regularity of the solution. Then we employ the Wong–Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory.
Mathematics Subject Classification: 65M60 / 65M15 / 65C30
Key words: Stochastic fractional diffusion equation / fractional Brownian sheet / Wong–Zakai approximation / finite element method / convolution quadrature / error analysis
© The authors. Published by EDP Sciences, SMAI 2025
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