Interior penalty discontinuous approximations of convection-diffusion problems with parabolic layers

A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for two-dimensional convection-diffusion problems with regular and parabolic layers. On an anisotropic Shishkin-type mesh with bilinear elements we prove error estimates (uniformly in the perturbation parameter) in an integral norm associated with this method. On different types of interelement edges we derive the values of discontinuity-penalization parameters. Numerical experiments complement the theoretical results.