In this paper, we deal with the numerical approximation of the coupled
wave equation of Kirchhoff type with nonlinear boundary damping and
memory term. Since the equation is a nonlinear equation, the
Raviart-Thomas mixed finite element method is one of the most suitable
techniques to obtain the approximated solution. In this paper, we will
show that using the Raviart-Thomas method the optimal convergence order
of the scheme can be achieved. To that end, we prove the necessary
lemmas and the main theorem. Finally, the efficiency of the method is
certified by numerical examples.