Numerical Analysis and Simulation for a Wave Equation with Dynamical Boundary Control

Abstract

This paper is concerned with a theoretical and numerical analysis for the stability of a vibrating beam of finite length which is fixed at one end and free at the other end and with a dynamical boundary control. On the theoretical results, we prove the existence and uniquenes of global solutions, and the stability of the total energy. Furthemore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time. Error estimates fot the semi-discrete and fully discrete schemes are provided and numerical experiments performed. From the numerical results, the rate of convergence are shoown to be consistent with the order of convegence expected from the theoretical ones.