Numerical studies of the damped Korteweg–de Vries system

We present a numerical analysis of the Korteweg–de Vries (KdV) system in a bounded interval under the effect of a localized damping mechanism. For the sake of completeness, we include the proofs of existence and uniqueness of the weak solution by means of the Faedo–Galerkin method. Error estimates of finite element approximations, for both semi-discrete and fully discrete schemes in the energy norm are provided and numerical experiments are performed.