  We study the numerical solution for Volerra integro-differential equations
with smooth and non-smooth kernels. We use a $h$-version discontinuous Galerkin
(DG) method and derive nodal error bounds that are explicit in the parameters
of interest. In the case of non-smooth kernel, it is justified that the
start-up singularities can be resolved at superconvergence rates by using
non-uniformly graded meshes. Our theoretical results are numerically validated
in a sample of test problems.
