论文标题
具有动态边界条件的Cahn- hilliard方程的错误估计值
Error estimates for the Cahn--Hilliard equation with dynamic boundary conditions
论文作者
论文摘要
在光滑域中，用Cahn--Hilliard-Hilliard-type动态边界条件给出了Cahn--hilliard方程的散装有限元半差异的融合证明。在弱公式中研究了半差异化作为二阶系统。 $ l^2 $和$ h^1 $规范中显示了最佳订单统一误差估计。错误估计基于一致性和稳定性分析。稳定性证明是基于利用二阶系统的反对称结构的能量估计来进行的。数值实验说明了理论结果。
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak formulation as a second order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$ and $H^1$ norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second order system. Numerical experiments illustrate the theoretical results.
