# Least-squares methods for the solution of fluid-structure interaction problems

**At LMSSC, Cnam, Paris, September 8th 2005**

Oliver Kayser-Herold (Doctorate, Institute of Scientific Computing, Technische Universität Braunschweig, Germany)

Different numerical methods have been proposed for the solution of partial differential equations (PDE). Most of them are based on a variational principle which recasts the PDE into an equivalent integral equation. One of the most common principles is the Galerkin method, which has some specific disadvantages for some types of PDE. In this talk an alternative variational principle, the least squares finite element method, will be tested with respect to its application for transient fluid-structure interaction problems.

After a short introduction of the basic ideas of the least squares finite element method (LSFEM), the used formulations for the Navier-Stokes equations and the equations of linear elastodynamics will be introduced with some numerical examples. Adding the interface conditions in a least squares sense then completes the coupled system. Finally a small example will be used to demonstrate the general possibility to solve strongly coupled fluid structure interaction problems with the least squares FEM.