Publications

We study the 2D linear wave equation with dynamical control on the boundary. New mathematical difficulties (https://www.sciencedirect.com/topics/mathematics/mathematical-difficulty) appear due to the boundary conditions. By adding some artificial viscosity (https://www.sciencedirect.com/topics/mathematics/artificial-viscosity) term, we introduce a penalized problem, and the well posedness (https://www.sciencedirect.com/topics/mathematics/posedness) is done by using the Faedo–Galerkin method. A numerical scheme (https://www.sciencedirect.com/topics/engineering/numerical-scheme) is proposed and the decay of the associated discrete energy is obtained. At the end, an a priori error (https://www.sciencedirect.com/topics/engineering/priori-error) estimate is obtained and some numerical results are presented.