论文标题
浸入有限元方法的稳定性和条件：分析和补救措施
Stability and conditioning of immersed finite element methods: analysis and remedies
论文作者
论文摘要
这篇评论论文讨论了过去十年中沉浸式或未固定有限元方法的发展。主要重点是分析和处理小切割元素的不良反应。我们区分了有关系统条件的稳定性和不利影响的不利影响，并概述了已发达的补救措施。特别是，我们提供了Schwarz预处理，元素聚集和幽灵惩罚表达的详细说明。此外，我们概述了针对正交和差异条件的弱执法而开发的方法，并讨论了开放的问题和未来的研究方向。
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse effects regarding the stability and adverse effects regarding the conditioning of the system, and we present an overview of the developed remedies. In particular, we provide a detailed explanation of Schwarz preconditioning, element aggregation, and the ghost penalty formulation. Furthermore, we outline the methodologies developed for quadrature and weak enforcement of Dirichlet conditions, and we discuss open questions and future research directions.
