SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1782-1813, August 2024.
Abstract. Finite element methods and kinematically coupled schemes that decouple the fluid velocity and structure displacement have been extensively studied for incompressible fluid-structure interactions (FSIs) over the past decade. While these methods are known to be stable and easy to implement, optimal error analysis has remained challenging. Previous work has primarily relied on the classical elliptic projection technique, which is only suitable for parabolic problems and does not lead to optimal convergence of numerical solutions for the FSI problems in the standard [math] norm. In this article, we propose a new stable fully discrete kinematically coupled scheme for the incompressible FSI thin-structure model and establish a new approach for the numerical analysis of FSI problems in terms of a newly introduced coupled nonstationary Ritz projection, which allows us to prove the optimal-order convergence of the proposed method in the [math] norm. The methodology presented in this article is also applicable to numerous other FSI models and serves as a fundamental tool for advancing research in this field.

中文翻译：

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薄结构相互作用的松耦合有限元方案的最优[数学]误差分析


《SIAM 数值分析杂志》，第 62 卷，第 4 期，第 1782-1813 页，2024 年 8 月。

抽象的。在过去的十年中，将流体速度和结构位移解耦的有限元方法和运动学耦合方案已被广泛研究用于不可压缩的流固相互作用（FSI）。虽然这些方法稳定且易于实施，但最佳误差分析仍然具有挑战性。先前的工作主要依赖于经典的椭圆投影技术，该技术仅适用于抛物线问题，并且不会导致标准[数学]范数下的FSI问题的数值解的最优收敛。在本文中，我们为不可压缩 FSI 薄结构模型提出了一种新的稳定全离散运动学耦合方案，并根据新引入的耦合非平稳 Ritz 投影建立了 FSI 问题数值分析的新方法，这使我们能够证明所提出方法在[数学]范数中的最优阶收敛。本文提出的方法也适用于许多其他 FSI 模型，并作为推进该领域研究的基本工具。