Abstract In this paper a novel application of the (high-order) H ( div ) -conforming Hybrid Discontinuous Galerkin finite element method for monolithic fluid-structure interaction (FSI) is presented. The Arbitrary Lagrangian Eulerian (ALE) description is derived for H ( div ) -conforming finite elements including the Piola transformation, yielding exact divergence free fluid velocity solutions. The arising method is demonstrated by means of the benchmark problems proposed by Turek and Hron (2006). With hp-refinement strategies singularities and boundary layers are overcome leading to optimal spatial convergence rates.

中文翻译：

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与符合 H(div) 的有限元的流固耦合

摘要 本文介绍了（高阶）H ( div ) 一致混合不连续伽辽金有限元方法在整体流固耦合 (FSI) 中的新应用。任意拉格朗日欧拉 (ALE) 描述是为符合 H ( div ) 的有限元导出的，包括 Piola 变换，产生精确的无发散流体速度解。通过 Turek 和 Hron (2006) 提出的基准问题证明了产生方法。通过 hp 细化策略，可以克服奇异点和边界层，从而实现最佳空间收敛率。