Uniform boundary stabilization for the finite difference semi-discretization of 2-D wave equation

Abstract

In this paper we treat the question of uniform exponential stability for the finite difference semi-discretization of 2-D wave equation with a boundary feedback. First we prove that the exponential decay of the discrete energy is not uniform (with respect to the mesh size) by showing that the constant of the observability inequality blows up. We prove after that adding a suitable vanishing numerical viscosity term leads to a uniform exponential decay of the energy.