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

Abstract

<abstract><p>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.</p></abstract>