On Discretization of the Evolution p-Bi-Laplace Equation

Abstract

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