论文标题
CAHN-带有动态边界条件的Hilliard类型方程的抽象错误分析
Abstract error analysis for Cahn--Hilliard type equations with dynamic boundary conditions
论文作者
论文摘要
这项工作解决了以数值为单位求解Cahn-Hilliard方程的问题。为此，我们引入了具有动态边界条件的Cahn-Hilliard类型方程的抽象公式，我们通过有限元素进行空间半差异，并根据能量估计技术证明误差界限。 Cahn-Hilliard/Cahn-Hilliard耦合的各种表述将适用于更大的抽象类别类别，类似于抛物线抛物线问题的通常弱表述。与非动态边界条件的问题相反，希尔伯特空间$ l^2（ω）$和$ h^1（ω）$与空间$ l^2（ω）\ times l^2（γ）$和$ \ lbrace v \ in H^1（ω）：γv\ in H^1（prace）因为我们正在考虑一个四阶微分方程，该方程将通过两个二阶微分方程的系统来描述，所以变化公式也由两个方程组成。
This work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization via finite elements and prove error bounds based on the technique of energy estimates. The variational formulation for Cahn-Hilliard/Cahn-Hilliard coupling, will apply to a larger abstract class of problems and is similar to the usual weak formulation of parabolic problems. In contrast to problems with non dynamic boundary conditions, the Hilbert spaces $L^2(Ω)$ and $H^1(Ω)$ are exchanged with the spaces $L^2(Ω)\times L^2(Γ)$ and $\lbrace v\in H^1(Ω): γv \in H^1(Γ)\rbrace$, respectively. Because we are considering a fourth-order differential equation, which will be described by a system of two second-order differential equations, the variational formulation also consists of a system of two equations.
