In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique of (iso)parametric mappings for which a level set representation of the evolving surface is essential. We derive basic results in which certain geometric characteristics of the exact space-time surface are related to corresponding ones of the numerical surface approximation. These results are used in a complete error analysis of a higher order space-time TraceFEM.

翻译：本文分析了一种用于演化曲面上标量曲面偏微分方程离散化的时空非拟合有限元方法。对于演化曲面的高阶逼近，我们采用了（等）参数映射技术，其中演化曲面的水平集表示至关重要。我们推导了基本结果，将精确时空曲面的某些几何特征与数值曲面逼近的相应特征联系起来。这些结果被用于一种高阶时空TraceFEM的完整误差分析中。