A new strategy for high-fidelity unsteady mesh adaptation dealing with fluid–structure interaction (FSI) problems is presented using a partitioned approach. The Euler equations are solved by an edge-based Finite-Volume solver whereas the linear elasticity equations are solved by the finite-element method using the Lagrange \mathbb P₁elements. The coupling between both codes is realized by imposing suitable boundary conditions on conforming meshes even at the fluid–structure interface. Small displacements of the structure are assumed and so the mesh is not deformed. The unsteady mesh adaptation process is based on a unique cavity operator which can handle non-manifold geometry, the fluid–structure interface in this work. The computation of a well-documented two-dimensional test case is finally carried out to perform validation of this new strategy as well as a three-dimensional test case to demonstrate our ability to treat complex three-dimensional test cases.