We consider a fictitious domain formulation for fluid-structure interaction problems based on a distributed Lagrange multiplier to couple the fluid and solid behaviors. How to deal with the coupling term is crucial since the construction of the associated finite element matrix requires the integration of functions defined over non-matching grids: the exact computation can be performed by intersecting the involved meshes, whereas an approximate coupling matrix can be evaluated on the original meshes by introducing a quadrature error. The purpose of this paper is twofold: we prove that the discrete problem is well-posed also when the coupling term is constructed in approximate way and we discuss quadrature error estimates over non-matching grids.

翻译：本文研究基于分布拉格朗日乘子的流体-结构相互作用问题虚拟域表述方法，该乘子用于耦合流体与固体行为。耦合项的处理至关重要，因为相关有限元矩阵的构建需要在非匹配网格上对函数进行积分：精确计算可通过相交网格实现，而近似耦合矩阵则可在原始网格上通过引入求积误差进行评估。本文目的有二：证明当耦合项以近似方式构建时离散问题仍是适定的，并讨论非匹配网格上的求积误差估计。