Least squares finite element methods for fluid-structure interaction problems

Abstract

The first order least squares finite element method is an alternative numerical procedure to standard Galerkin methods for the solution of partial differential equations. Its advantages are mainly the resulting symmetric positive definite matrices and the inherent numerical stability. Several first order formulations were proposed for the incompressible Navier–Stokes equations and for the equations of linear elasticity. Here we analyse which of these methods could provide an efficient and accurate tool for the solution of fluid-structure interaction problems. It seems that the combination of inherent least squares stability and high order ansatz functions is very promising.