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Journal Articles AIMS Mathematics Year : 2022

An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise

Xiao Qi
  • Function : Author
Can Huang
  • Function : Author
Chuanju Xu
  • Function : Author

Abstract

In this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded $ \log $-Whittle-Mat$ \acute{{\mathrm{e}}} $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.

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Dates and versions

hal-03962943 , version 1 (30-01-2023)
hal-03962943 , version 2 (03-02-2023)

Licence

Attribution - CC BY 4.0

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Xiao Qi, Mejdi Azaiez, Can Huang, Chuanju Xu. An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise. AIMS Mathematics, 2022, 7 (12), pp.20684-20710. ⟨10.3934/math.20221134⟩. ⟨hal-03962943v1⟩
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