In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time have been introduced. For geometrically higher order accuracy a parametric mapping on a background space-time tensor-product mesh has been used. In this paper, we concentrate on the geometrical accuracy of the approximation and derive error bounds for the distance between the realized and an ideal mapping in different norms and derive results for the space-time regularity of the parametric mapping. These results are important for the error analysis of corresponding unfitted space-time finite element methods.

翻译：在[Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165]中，针对移动域上的偏微分方程，引入了在空间和时间上具有高阶精度的新型几何非拟合时空有限元方法。为实现几何高阶精度，采用了基于背景时空张量积网格的参数映射。本文重点关注近似的几何精度，推导了实现映射与理想映射在不同范数下距离的误差界，并给出了参数映射的时空正则性结果。这些结果对于相应的非拟合时空有限元方法的误差分析具有重要意义。