Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise
A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence,...
Saved in:
| Published in: | IMA journal of numerical analysis Vol. 42; no. 3; pp. 2301 - 2335 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
22-07-2022
|
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence, uniqueness and regularity results, we approximate the noise with the piecewise constant function in time, in order to obtain a regularized stochastic fractional subdiffusion problem. The regularized problem is then approximated by using the finite element method in spatial direction. The mean squared errors are proved based on the sharp estimates of the various Mittag–Leffler functions involved in the integrals. Numerical experiments are conducted to show that the numerical results are consistent with the theoretical findings. |
|---|---|
| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drab035 |