On the stability and conditioning of a fictitious domain formulation for fluid-structure interaction problems

Abstract: We consider a distributed Lagrange multiplier formulation for fluid-structure interaction problems in the spirit of the fictitious domain approach. Our previous studies showed that the formulation is unconditionally stable in time and that its mixed finite element discretization is well-posed. In this paper, we analyze the behavior of the condition number with respect to mesh refinement. Moreover, we observe that our formulation does not need any stabilization term in presence of small cut cells and conditioning is not affected by the interface position.