A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

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Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation (2005, methodology): “Numerical experiments demonstrating the performance of the proposed approach will be presented.”
Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, background): “Although there are some works [2,8,28,59,66,76,86,87] on error estimates for hyperbolic conservation law and parabolic problems, there are only a few works in the literature for error estimates of the LDG method for nonlinear wave equations with high order derivatives.”
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows (2003, background): “Other researchers in the area include S€ uli and co-workers [18,24,47], Larson and Barth [25], and Formaggia et al.”
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”
hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. (2002, methodology): “The aim of this section is to develop the a posteriori and a priori error analysis for general linear target functionals J(·) of the solution; for related work, we refer to [7, 10, 16, 17, 25], for example.”