Analysis of Discontinuous Galerkin Methods using Mesh-Dependent Norms   and Applications to Problems with Rough Data
  We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine a problem with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control. 
Emmanuil H. Georgoulis and Tristan Pryer
math.NA