论文标题
相位场晶体方程的C0内部惩罚方法
A C0 Interior Penalty Method for the Phase Field Crystal Equation
论文作者
论文摘要
我们为第六阶相晶体方程提供了C0内部惩罚有限元法。我们证明了数值方案是可解决的，无条件的能量稳定和收敛性。我们指出，本文的新颖性在于这是为相晶晶方程开发的第一个C0内部惩罚有限元方法。此外，提出的错误分析开发了一种详细的方法，用于分析使用C0内部惩罚方法分析时间依赖性问题。我们进一步基准了我们针对先前在文献中建立的数值实验的方法。
We present a C0 interior penalty finite element method for the sixth-order phase field crystal equation. We demonstrate that the numerical scheme is uniquely solvable, unconditionally energy stable, and convergent. We remark that the novelty of this paper lies in the fact that this is the first C0 interior penalty finite element method developed for the phase field crystal equation. Additionally, the error analysis presented develops a detailed methodology for analyzing time dependent problems utilizing the C0 interior penalty method. We furthermore benchmark our method against numerical experiments previously established in the literature.
