  In this article, we analyze and numerically assess a new fictitious domain
method for fluid-structure interactions in two and three dimensions. The
distinguishing feature of the proposed method is that it only solves for one
velocity field for the whole fluid-structure domain; the interactions remain
decoupled until solving the final linear algebraic equations. To achieve this
the finite element procedures are carried out separately on two different
meshes for the fluid and solid respectively, and the assembly of the final
linear system brings the fluid and solid parts together via an isoparametric
interpolation matrix between the two meshes. In this article, an implicit
version of this approach is introduced. The property of energy conservation is
proved, which is a strong indication of stability. The solvability and error
estimate for the corresponding stationary problem (one time step of the
transient problem) are analyzed. Finally, 2D and 3D numerical examples are
presented to validate the conservation properties.

Numerical Analysis;Computational Engineering, Finance, and Science