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 fluidstructure 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.
immersed finite element method fluid structure interaction numerical stability cfl condition