  In this work we present an a posteriori analysis for classes of inconsistent,
nonconforming schemes approximating elliptic problems. We show the estimates
coincide with existing ones for interior penalty type discontinuous Galerkin
approximations of the Laplacian and give new estimates for inconsistent
discontinuous Galerkin approximation schemes of elliptic problems under
quadrature approximation. We also examine the effect of inconsistencies on the
a posteriori analysis of schemes applied to an unbalanced problem.
