A Review of Finite Element Methods for Fluid-Structure Interactions

We present a comprehensive review of finite element methods (FEM) for solving fluid–structure interaction (FSI) problems. Our aim is to systematically categorise and compare these methods based on three key aspects: mesh type, coupling strategy, and the choice of solved variables. For each method, we highlight its respective advantages and limitations. In addition, we formulate and compare the finite element weak forms of the various approaches, employing Newton’s method to linearise nonlinear terms at the continuous functional level. We implement six FSI methods in the open-source software package FreeFEM++, and compare these methods based on three benchmarks.