AI 中文总结
该研究用有限元方法离散线性化Cahn-Hilliard-Cook方程的空间变量，结合向后欧拉时间步进，在特定假设下证明强收敛估计，得到对应确定性方程的误差界，为非线性方程温和解的近似提供支撑。
AI 中文摘要
采用标准有限元方法对线性化Cahn-Hilliard-Cook方程的空间变量进行离散化；在驱动该方程的维纳过程的协方差算子满足适当假设的条件下，证明了强收敛估计；同时研究了向后欧拉时间步进方法，分析基于解析半群框架展开；主要工作是证明对应确定性Cahn-Hilliard方程的详细误差界，所得结果可解释为对随机卷积的近似结果，而随机卷积是非线性Cahn-Hilliard-Cook方程温和解的一部分。
英文摘要
The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main effort is spent on proving detailed error bounds for the corresponding deterministic Cahn-Hilliard equation. The results should be interpreted as results on approximation of the stochastic convolution, which is a part of the mild solution of the nonlinear Cahn-Hilliard-Cook equation.
Journal refIMA Journal of Numerical Analysis, Volume 31, Issue 4, October 2011, Pages 1315 1333
