Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data
journal contributionposted on 17.01.2018, 10:10 by Emmanuil H. Georgoulis, Tristan Pryer
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 some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control.