AI 中文总结
本文对用于带变形界面流固耦合问题的半离散浸入CutFEM开展严格误差分析，证明k≥3时流体速度、固体位移和流体压力的收敛阶，属该类非拟合有限元方法的首次收敛分析。
AI 中文摘要
我们对应用于流固耦合（FSI）问题的半离散浸入CutFEM进行了严格的误差分析，该问题涉及不可压缩粘性流体与弹性固体。该方法采用拉格朗日乘子来实现流固耦合条件，同时充分考虑结构变形对流体域的影响。对于足够正则的FSI解及次数k≥3的有限元，我们证明了流体速度和固体位移在与FSI问题相关的能量范数下具有k阶收敛性，流体压力具有k-1阶收敛性。据我们所知，这是针对带变形界面的全耦合FSI系统的非拟合有限元方法的首次严格收敛分析。
英文摘要
We present a rigorous error analysis for a semidiscrete immersed CutFEM applied to fluid--structure interaction (FSI) problems involving an incompressible viscous fluid and an elastic solid. The method employs a Lagrange multiplier to enforce the fluid-solid coupling conditions while fully accounting for the effect of the structural deformation on the fluid domain. For sufficiently regular FSI solutions and finite elements of degree $k\geq3$, we prove convergence of order $k$ for the fluid velocity and solid displacement and convergence of order $k-1$ for the fluid pressure in the energy norms associated with the FSI problem. To the best of our knowledge, this is the first rigorous convergence analysis of an unfitted finite element method for a fully coupled FSI system with a deforming interface.
