  We present sharp and sufficient bounds for the interior penalty term and time
step size to ensure stability of the Symmetric Interior Penalty Discontinuous
Galerkin (SIPDG) method combined with an explicit time-stepping scheme. These
conditions hold for generic meshes, including unstructured non-conforming
heterogeneous meshes of mixed element types, and apply to a large class of
linear hyperbolic problems, including the acoustic wave equation, the
(an)isotropic elastic wave equations and Maxwell's equations. The penalty term
bounds are computed element-wise, while bounds for the time step size are
computed at weighted submeshes requiring only a small number of elements and
faces. Numerical results illustrate the sharpness of these bounds.
