An application of moment method to uniform boundary controllability property of a semidiscrete 1-d wave equation with a lower rate vanishing viscosity.

We use the moment method in order to study the uniform boundary controllability of a semidiscrete 1-d wave equation, when a lower rate numerical vanishing viscosity term is added. The high frequency spurious oscillations introduced by the classical method of space discrete numerical schemes lead to nonuniform controllability properties, which are dumped out using an additional vanishing viscosity term. Our extra numerical viscosity is weaker than the one used in [30] , but enough in order to treat high frequency numerical spurious oscillations. Hence, we are able to prove the convergence of the sequence of discrete controls to a control of the continuous wave equation, when the mesh size tends to zero. [ABSTRACT FROM AUTHOR]