A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

By Ohannes A. Karakashian, Frédéric Pascal. SIAM Journal on Numerical Analysis, 2003

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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.”
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics (2010, neutral): “11b) follows similarly to [28,38].”
Compact embeddings of broken Sobolev spaces and applications (2009, methodology): “Reconstruction operator As is the case in many works on discontinuous Galerkin methods, ranging from a posteriori error estimation [12] to the proof of broken Poincaré type inequalities [5, 6, 14, 18], we require at several points a continuous reconstruction operator.”
hp analysis of a hybrid DG method for Stokes flow (2013, methodology): “For the proof of efficiency, we utilize an averaging operator of Oswald-type [52, 40], which allows to construct a conforming approximation for the finite element solution by local postprocessing.”