On computational issues of immersed finite element methods

The objective of this paper is to provide a review of recent finite element formulations for immersed methods. In these finite element formulations, independent Lagrangian solid meshes are introduced to move on top of a background Eulerian fluid mesh. This key feature allows the handling, without excessive fluid mesh adaptation, multiple deformable solids immersed in viscous fluid. In particular, pros and cons of both explicit and implicit approaches are illustrated along with subtle differences between incompressible and slightly compressible models.