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.

翻译：我们为六阶场水晶方程式提出了一个C0内限刑罚元素法。我们证明数字法是独一无二的可溶性、无条件的能源稳定性和趋同性。我们指出,本文的新颖之处在于这是为分场水晶方程式开发的第一种C0内限刑罚元素法。此外,提出的错误分析还制定了详细的方法,利用C0内限处罚法分析与时间相关的问题。我们进一步参照文献中先前确定的数字实验来衡量我们的方法。