We present a monolithic finite element formulation for (nonlinear) fluid-structure interaction in Eulerian coordinates. For the discretization we employ an unfitted finite element method based on inf-sup stable finite elements. So-called ghost penalty terms are used to guarantee the robustness of the approach independently of the way the interface cuts the finite element mesh. The resulting system is solved in a monolithic fashion using Newton's method. Our developments are tested on a numerical example with fixed interface.

翻译：我们提出了一种基于欧拉坐标的（非线性）流固耦合问题整体式有限元方法。在离散化过程中，采用基于inf-sup稳定有限元的非拟合有限元方法。通过引入所谓的"幽灵罚项"来确保该方法对界面切割有限元网格的方式具有鲁棒性。最终形成的系统采用牛顿法进行整体求解。我们通过一个固定界面的数值算例对所提出的方法进行了验证。