SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 797-828, January 2021.
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid a mesh regeneration procedure when solving moving interface problems. Despite the various applications in moving interface problems, a complete theoretical study on the convergence behavior is still missing. This research is devoted to closing the gap between numerical experiments and theory. We present the first fully discrete analysis including the stability and optimal error estimates for a backward Euler IFE method for solving parabolic moving interface problems. Numerical results are also presented to validate the analysis.

中文翻译：

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用不适合网格物体上的动态浸入空间解决抛物线运动界面问题：完全离散分析

SIAM数值分析杂志，第59卷，第2期，第797-828页，2021年1月。浸入式
有限元（IFE）方法是解决不匹配网格上的界面问题的一组长期存在的数值方法。这些方法的核心论点是在解决移动界面问题时避免网格再生程序。尽管在移动接口问题中有各种应用，但仍缺少关于收敛行为的完整理论研究。这项研究致力于缩小数值实验和理论之间的差距。我们提出了第一个完全离散的分析，包括用于求解抛物线运动界面问题的后向Euler IFE方法的稳定性和最佳误差估计。还提供了数值结果以验证分析。