Abstract The numerical approximation of incompressible fluid–structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability, but at the expense of solving a computationally demanding coupled system at each time step. For the case of the coupling with immersed thin-walled solids, we introduce a class of semi-implicit coupling schemes that avoids strongly coupling without compromising stability and accuracy. A priori energy and error estimates are derived. The theoretical results are illustrated through numerical experiments in an academic benchmark.

中文翻译：

---

具有浸入式薄壁结构的 FSI 的拉格朗日乘子公式的分裂方案：稳定性和收敛性分析

摘要 用拉格朗日乘子对不可压缩流固耦合问题进行数值逼近一般基于强耦合格式。这提供了无条件的稳定性，但以在每个时间步求解计算要求高的耦合系统为代价。对于与浸入式薄壁固体耦合的情况，我们引入了一类半隐式耦合方案，该方案在不影响稳定性和准确性的情况下避免了强耦合。推导出先验能量和误差估计。通过学术基准中的数值实验说明了理论结果。