  In this paper, we consider a structurally damped elastic equation under
hinged boundary conditions. Fully-discrete numerical approximation schemes are
generated for the null controllability of these parabolic-like PDEs. We mainly
use finite element method (FEM) and finite difference method (FDM)
approximations to show that the null controllers being approximated via FEM and
FDM exhibit exactly the same asymptotics of the associated minimal energy
function. For this, we appeal to the theory originally given by R. Triggiani
[20] for construction of null controllers of ODE systems. These null
controllers are also amenable to our numerical implementation in which we
discuss the aspects of FEM and FDM numerical approximations and compare both
methodologies. We justify our theoretical results with the numerical
experiments given for both approximation schemes.
