论文标题
随机Cahn-Hilliard方程的后验估计值
Robust a posteriori estimates for the stochastic Cahn-Hilliard equation
论文作者
论文摘要
我们得出了随机Cahn-Hilliard方程的完全离散有限元近似的后验误差估计。通过将方程式分解为线性随机偏微分方程（SPDE）和非线性随机偏微分方程（RPDE）来获得A后验结合。所得估计值相对于界面宽度参数是可靠的，并且是可计算的，因为它涉及线性（随机）Cahn-Hilliard操作员的离散主特征值。此外，估计值在拓扑变化以及随机噪声的强度方面是可靠的。我们提供数值模拟，以证明所提出的自适应算法的实用性。
We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial differential equation (SPDE) and a nonlinear random partial differential equation (RPDE). The resulting estimate is robust with respect to the interfacial width parameter and is computable since it involves the discrete principal eigenvalue of a linearized (stochastic) Cahn-Hilliard operator. Furthermore, the estimate is robust with respect to topological changes as well as the intensity of the stochastic noise. We provide numerical simulations to demonstrate the practicability of the proposed adaptive algorithm.
