Finite element error estimation for quasi-Newtonian fluid-structure interaction problems

We consider a monolithic scheme for fluid-structure interaction problems involving an incompressible quasi-Newtonian fluid. The monolithic formulation is obtained using the Arbitrary Lagrangian Eulerian (ALE) method with matching conditions at the fluid-structure interface. The stability and error analysis are performed for the finite element approximation. Finally, some numerical experiments that confirm the theoretical analysis are presented.