In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time discretisation. Our analysis relies on a specific geometric assumption on the evolution of the surface. Our main results are $L^2_{H^1}$ error bounds for both the semi-discrete and fully discrete schemes, and we provide some numerical results.

翻译：本文研究了具有对数势的Cahn-Hilliard方程的半离散与全离散演化曲面有限元格式。具体而言，我们采用线性有限元进行空间离散，并应用后向欧拉法进行时间离散。我们的分析依赖于曲面演化过程中的特定几何假设。主要结果为半离散与全离散格式的$L^2_{H^1}$误差估计，并提供了若干数值计算结果。