Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations

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Symmetric Interior Penalty DG Methods for the CompressibleNavier-Stokes Equations I: Method Formulation (2005, methodology): “Finite element methods, discontinuous Galerkin methods, compressible Navier– Stokes equations”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “In addition, Giles and Pierce [15] [16] describe adjoint correction techniques and Giles and Süli [17] review a posteriori output-error estimation for finite element methods applied to linear and nonlinear partial differential equations relevant to CFD. Hartmann and Houston also provide a recent ove”
A simple shock‐capturing technique for high‐order discontinuous Galerkin methods (2012, background): “Here, the 2D (planar) case is considered [43].”
Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation (2005, methodology): “of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier– Stokes equations.”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, background): “In [87] the authors use the magnitude of the residual to determine the amount of artificial viscosity added to the shock region.”