This paper addresses the approximation of surface diffusion flow using Cahn–Hilliard-type models. We introduce and analyze a new variational phase field model that associates the classical Cahn–Hilliard energy with two degenerate mobilities and guarantees a second-order accuracy in the approximation of the sharp limit. We also introduce simple and efficient numerical schemes to approximate the solutions to three Cahn–Hilliard-type models for surface diffusion flow, including the one we propose, and we provide 2D and 3D numerical experiments that illustrate the advantages of our approach.

中文翻译：

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表面扩散流的近似：具有退化迁移率的二阶变分 Cahn-Hilliard 模型

本文使用 Cahn-Hilliard 型模型解决了表面扩散流的近似问题。我们引入并分析了一种新的变分相场模型，该模型将经典的 Cahn-Hilliard 能量与两种简并迁移率相关联，并保证了近似锐极限的二阶精度。我们还引入了简单有效的数值方案来近似解决表面扩散流的三个 Cahn-Hilliard 型模型，包括我们提出的模型，并且我们提供了 2D 和 3D 数值实验来说明我们方法的优势。