An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise
In this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded log-Whittle-Mate´rn (W-M) random diffusion coefficient field and Q-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness,...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-09-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20221134?viewType=HTML |
| Summary: | In this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded log-Whittle-Mate´rn (W-M) random diffusion coefficient field and Q-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness, and stability of the mild solution. A sampling approach called approximation circulant embedding with padding is proposed to sample the random coefficient field. Then a spatio-temporal discretization method based on semi-implicit Euler-Maruyama scheme and finite element method is constructed and analyzed. An estimate for the strong convergence rate is derived. Numerical experiments are finally reported to confirm the theoretical result. |
|---|---|
| ISSN: | 2473-6988 |