Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems

By Paul Houston, Christoph Schwab, Endre Süli. SIAM Journal on Numerical Analysis, 2001

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Optimal BV estimates for a discontinuous Galerkin method for linear elasticity (2004, background): “Perugia, and Sch¨ otzau [9], and Houston, Schwab, and S¨ uli [ 18 ], where the scalar Poisson”
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes (2016, unknown): “This coincides with the analogous result derived in [36] for standard meshes consisting of simplices or tensorproduct elements.”
Estimation of penalty parameters for symmetric interior penalty Galerkin methods (2007, methodology): “Another related discontinuous Galerkin method is the non-symmetric interior penalty Galerkin (NIPG) method [21] [15]: this method differs from the SIPG method by only one sign: the symmetrizing term is added instead of being subtracted.”
On 2D elliptic discontinuous Galerkin methods (2006, unknown): “References [10–15]).”
ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS (2007, methodology): “Finally, we mention that the extension of our hp-version a posteriori error analysis to the Stokes equations of incompressible fluid flow can be found in the recent conference paper [ 22 ].”
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows (2013, unknown): “2)], and [22], respectively.”