论文标题
能量稳定的线性扩散曲柄 - 纽科森方案，用于Cahn-Hilliard梯度流动
An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow
论文作者
论文摘要
我们提出和分析了针对Cahn-Hilliard梯度流量的线性稳定的半密码扩散曲柄 - Nicolson方案。在此方案中，非线性散装力以两个二阶稳定项明确处理。这种处理导致线性椭圆系统具有恒定系数和可证明的离散能量耗散。对完全离散的方案进行了严格的误差分析。当时间尺寸和空间尺寸足够小时，使用二阶阶段的二阶准确度是通过由$ 1/\ varepsilon $控制的预制器控制的。 {这是$ \ varepsilon $是接口的厚度}。提出了数值结果以及自适应时间步进，以验证所提出的方案的准确性和效率。
We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation. Rigorous error analysis is carried out for the fully discrete scheme. When the time step-size and the space step-size are small enough, second order accuracy in time is obtained with a prefactor controlled by some lower degree polynomial of $1/\varepsilon$. {Here $\varepsilon$ is the thickness of the interface}. Numerical results together with an adaptive time stepping are presented to verify the accuracy and efficiency of the proposed scheme.
