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 rigorous 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 and lay the ground for the error analysis of corresponding unfitted space-time finite element methods.

翻译：在文献[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，提出了具有空间与时间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，该方法在背景时空张量积网格上采用了参数映射。本文聚焦于逼近的几何精度，推导了实现映射与理想映射在不同范数下距离的严格界值，并得到了参数映射的时空正则性结果。这些结论至关重要，为相应非拟合时空有限元方法的误差分析奠定了基础。