  In this paper, numerical experiments are carried out to investigate the
impact of penalty parameters in the numerical traces on the resonance errors of
high order multiscale discontinuous Galerkin (DG) methods [6, 7] for
one-dimensional stationary Schr\"{o}dinger equation. Previous work showed that
penalty parameters were required to be positive in error analysis, but the
methods with zero penalty parameters worked fine in numerical simulations on
coarse meshes. In this work, by performing extensive numerical experiments, we
discover that zero penalty parameters lead to resonance errors in the
multiscale DG methods, and taking positive penalty parameters can effectively
reduce resonance errors and make the matrix in the global linear system have
better condition numbers.
