  We propose a cheaper version of \textit{a posteriori} error estimator from
arXiv:1707.00057 for the linear second-order wave equation discretized by the
Newmark scheme in time and by the finite element method in space. The new
estimator preserves all the properties of the previous one (reliability,
optimality on smooth solutions and quasi-uniform meshes) but no longer requires
an extra computation of the Laplacian of the discrete solution on each time
step.
