Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

By Jan S. Hesthaven, Tim Warburton. 2007

2,270 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7ba384d36072ddc1bb925b1a0867c4b3e4ed28a8

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Citations in the corpus

Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations (2011, methodology): “…i c l e i n f o Article history: Received 21 January 2011 Received in revised form 29 April 2011 Accepted 19 August 2011 Available online 28 August 2011 Keywords: High order methods Discontinuous Galerkin Energy stability Flux reconstruction Filter 0045-7825/$ - see front matter 2011 Elsevier B.V.”
Slope limiting for discontinuous Galerkin approximations with a possibly non‐orthogonal Taylor basis (2013, background): “The DG formulation for general conservation laws is described, for example, in [2, 4, 7].”
On the accuracy of high-order discretizations for underresolved turbulence simulations (2013, unknown): “the book of Hesthaven and Warburton [20].”
A high‐order hybridizable discontinuous Galerkin method for elliptic interface problems (2013, methodology): “On these meshes, we consider polynomials of degree k to represent all the approximate variables using a nodal basis within each element [26].”
A unified approach for a posteriori high-order curved mesh generation using solid mechanics (2016, methodology): “The performance of high-order discretisation methods for the simulation of various problems in science and engineering has been the object of intensive research during the last twodecades [32,41,44,67].”
Explicit Discontinuous Galerkin methods for unsteady problems (2012, methodology): “A very efficient implementation of an explicit DG scheme on tetrahedral elements is described by Hesthaven [22], where a nodal complete order basis is chosen and all fluxes are approximated by collocation on the element nodes.”