Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data (Q1697293)

The paper deals with the numerical solution of the Poisson problem with rough data, i.e., the right-hand side \(f\in H^{-2}(\Omega)\setminus H^{-1}(\Omega)\). The problem is discretized by the interior penalty Galerkin method. The authors prove the inf-sup stability condition in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. Numerical examples justifying the theoretical error estimates are presented.