In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis.

中文翻译：

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移动表面上对流-扩散方程的扩散界面方法的稳定性和误差分析

在本文中，我们分析了求解移动表面抛物线偏微分方程的完全离散数值方案。该方法基于漫反射界面方法，该方法涉及移动表面的水平集描述。在空间网格大小、时间步长和界面宽度的合适条件下，我们获得了相对于自然范数的稳定性和误差界限。此外，我们提供了验证我们分析的测试计算。