In this article, we implement and analyze a locally modified parametric finite element method for fluid structure interaction problems using LBB-stable finite elements. The variational formulation of the monolithically coupled fluid structure interaction problems is solved using a fully Eulerian framework. A combination of $Q_2\text{-}{Q}_2\text{-}(Q_1\text{+}{Q}_0^{dc})$ and $P_2\text{-}{P}_2\text{-}(P_1\text{+}{P}_0^{dc⁎})$ finite elements are used to approximate the globally defined velocity-displacement-pressure fields. The edges of the grid cells through which interface is passing, are re-aligned to ensure that interface geometry is captured by the grid efficiently. Values of degrees of freedom corresponding to nodes belonging to such cells are updated using Galerkin projection. The numerical simulation results of the new framework were found to be in good agreement with standard benchmark problem data and reference values. The finite element framework was also extended and tested for adaptive grid refinement.

在本文中，我们使用LBB稳定有限元实现并分析了针对流体结构相互作用问题的局部修改参数有限元方法。使用完全欧拉框架解决了整体耦合流体结构相互作用问题的变式。组合${问}_2\text{--}{问}_2\text{--}（{问}_{\mathrm{1个}}\text{+}{问}_0^{dC}）$ 和 $P_2\text{--}{P}_2\text{--}（P_{\mathrm{1个}}\text{+}{P}_0^{dC⁎}）$有限元用于近似全局定义的速度-位移-压力场。重新对齐界面所经过的网格单元的边缘，以确保界面几何有效地被网格捕获。使用Galerkin投影来更新与属于此类单元的节点相对应的自由度的值。发现新框架的数值模拟结果与标准基准问题数据和参考值非常吻合。有限元框架也得到了扩展，并进行了自适应网格优化的测试。