  In this article, the energy stability of a one-field fictitious domain method
is proved and validated by numerical tests in two and three dimensions. The
distinguishing feature of this 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. The weak formulations are introduced in the
continuous case and after discretization in time. Then the stability is
analyzed through an energy estimate. Finally, numerical examples are presented
to validate the energy stability properties.
