论文标题
通过在未固定网格上使用动态沉浸空间解决抛物线移动界面问题：完全离散的分析
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
论文作者
论文摘要
沉浸有限元（IFE）方法是一组长期存在的数值方法，用于解决未固定网格上的界面问题。该方法的核心论点是在解决移动接口问题时避免网格再生过程。尽管在移动界面问题中有各种应用，但关于收敛行为的完整理论研究仍然缺失。这项研究致力于缩小数值实验与理论之间的差距。我们提出了第一个完全离散的分析，包括用于求解抛物线移动接口问题的稳定性和最佳误差估计。还提出了数值结果以验证分析。
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 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 close 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.
