An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise
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In this paper, we investigate the stochastic evolution equations (SEEs) driven by log-Whittle-Matérn (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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