论文标题
由随机扩散系数和乘法噪声驱动的随机进化PDE的有效数值方法
An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise
论文作者
论文摘要
在本文中，我们研究了由$ \ log $ -whittle-whittle-mat $ \急性{\ mathrm {e}} $ rn（w-m）随机扩散系数和$ q $ -Wienter乘数强力噪声驱动的随机进化方程（See）。首先，通过证明温和解决方案的存在，独特性和稳定性来确定基础方程的良好性。提出了一种带有填充物嵌入近似循环液的抽样方法，以采样随机系数场。然后，构建和分析了基于半无限欧拉山山和有限元方法的时空离散方法和有限元方法。得出了强收敛速率的估计值。最终报告了数值实验以确认理论结果。
In this paper, we investigate the stochastic evolution equations (SEEs) driven by $\log$-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.
