A least‐squares finite element approach to model fluid‐structure interaction problems

Abstract

In this contribution an approach to model fluid-structure interaction (FSI) problems with monolithic coupling is presented. The fluid as well as the structural domain are discretized using the least-squares finite element method (LSFEM), whose application results in a minimization problem with symmetric positive definite systems also for non self-adjoint operators, see e.g. [2]. In this study, the second-order systems are reduced to first-order systems by introducing new variables, which leads to least-squares formulations for both domains based on the stresses and velocities as presented in e.g.[5] and [7]. A conforming discretization of the unknown fields in H 1 and H(div) using Lagrange interpolation polynomials and vector-valued Raviart-Thomas interpolations functions, respectively, leads to the inherent fulfillment of the FSI coupling conditions. In more detail, a discretization in H 1 ensures continuity of the velocity field and a discretization in H(div) results in continuity of the normal stress components at the interface.