Comparison between numerical methods applied to the damped wave equation

Abstract

For the numerical solution of Dirichlet-Neumann problems related to 1D damped wave propagation, from a numerical point of view, we compare the so-called energetic approach, considered here separately for boundary and finite element methods with classical finite difference schemes, both explicit and implicit. The analysis reveals the superiority of energetic approximations with respect to unconditional stability and accuracy with respect to any choice of discretization parameters.