Discretization for a 2D-viscoelastic wave equation with dynamic boundary conditions

This article presents and analyzes a finite element approach for the 2D-viscoelastic wave equation with dynamic boundary conditions and strong damping. We use the Faedo–Galerkin method to prove the global existence of solutions and the multiplier approach to determine the asymptotic behavior in a bounded domain. We show and analyze typical semi-discrete systems as well as an implicit fully discrete scheme. For both semi-discrete and fully discrete methods, optimal a priori error estimates are demonstrated. Finally, some numerical findings and a priori error estimate are derived.