Since the Navier-Stokes equations for fluid flow are nonlinear, problems involving fluids enclosed in elastic solid are difficult and only the simplest of problems can be solved with analytical solutions. Current computational methods commonly use iteration with separate treatment for the solid and the fluid. This dissertation presents a method used to solve for a global velocity field in the fluid and solid in once coupled linear system. The existence and uniqueness of a solution to this problem is established. The finite element mixed method is used for spatial discretization and a finite difference scheme is applied to discretize the problem in the time variable.
Error estimates for a finite element approximation and for a global discretization are derived.
The discretization involves a global treatment of the velocity and pressure which leads to a linear system with block structured matrix. Results of numerical experiments are provided.