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 $-Whittle-Mat$ \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 pro...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 12; pp. 20684 - 20710
Main Authors Qi, Xiao, Azaiez, Mejdi, Huang, Can, Xu, Chuanju
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
Engineering Sciences
Materials
q-wiener multiplicative noise
random coefficient
sees
strong convergence
Random coefficient
Strong convergence
Q -Wiener multiplicative noise
SEEs
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ISSN2473-6988
2473-6988
DOI10.3934/math.20221134

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20221134