On the discretization of evolution $p$-bi-Laplace equation

This article discusses the mixed finite element method combined with backward-Euler method to study the hyperbolic $p$-bi-Laplace equation, where the existence and uniqueness of solution for discretized problem is shown in Lebesgue Sobolev spaces. The mixed formulation and the inf–sup condition are then given to prove the well posed of the scheme and the optimal a priori error estimates for fully discrete schemes is extracted. Finally, a numerical example is given to confirm the theoretical results obtained.