Adaptive Finite Element Approximation of Hyperbolic Problems

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Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation (2005, background): “For a more detailed discussion, we refer to the review articles [6, 19].”
hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. (2002, methodology): “For a recent review of hp–refinement strategies, we refer to [14]; see also [1, 4, 16, 23, 25] for related work.”
Symmetric Interior Penalty DG Methods for the CompressibleNavier-Stokes Equations I: Method Formulation (2005, background): “In particular, the key focus of these articles was the derivation of so–called ‘goal–oriented’ a posteriori error bounds together with the design of corresponding adaptive mesh refinement algorithms in order to yield guaranteed error control; for the generalization of these ideas to the hp–version o”
A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs (2007, methodology): “The hp-adaptive meshes are constructed by first marking the elements for refinement/derefinement according to the size of the local error indicators ηκ ; this is achieved by employing the fixed fraction strategy, see [27], with refinement and derefinement fractions set to 25% and 10%, respectively.”