On the stability of the Immersed Finite Element Method with high order structural elements

The Immersed Finite Element Method (IFEM) is a mathematical formulation for fluid–structure interaction problem like the Immersed Boundary Method; in IFEM the immersed structure has the same space dimension of the fluid domain. We present a stability of IFEM for a scheme where the Dirac delta distribution is treated variationally, as in [1]; moreover the finite element space related to the structure displacement consists of piecewise continuous Lagrangian elements, at least quadratic. The analysis is performed on two different time-stepping scheme. We demonstrate also that when the structure density is smaller than the fluid one, the stability is assured only if the time step size is bounded from below.

► We give a stability criteria when using structural high order finite element.
► Explicit algorithm is stable under a CFL condition.
► Implicit algorithm is always stable.
► When ρs ⩽ ρf for implicit algorithm time step is limited from below for stability.