ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

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A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems (2010, background): “For ease of presentation, let us make some simplifying assumptions.”
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows (2013, unknown): “Numerical experiments are presented, which demonstrate the performance of the proposed algorithm.”
An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems (2011, background): “Some ideas from a posteriori analyses for the Poisson problem presented in [4, 21, 20, 1, 9] are also implicitly utilized here in the context of fourth order problems.”
hp analysis of a hybrid DG method for Stokes flow (2013, methodology): “Similar results for quadrilateral and hexahedral meshes or for the two dimensional case can be found in [15] and [36]; see also [7, 45] for the related construction of hp approximations.”
A robust a-posteriori error estimator for discontinuous Galerkin methods for convection--diffusion equations (2009, methodology): “Our analysis is based on the approach in [18] where energy norm a-posteriori error estimates were developed for pure diffusion problems.”