Discontinuous Galerkin Methods: Theory, Computation and Applications

By Bernardo Cockburn, G. Em Karniadakis, Chi-Wang Shu. 2011

650 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/afbd4e1cf02a83c44fa7213641cf741c7d0c5636

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Citations in the corpus

A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems (2010, background): “All rights reserved List of AICES technical reports: http://www.aices.rwth-aachen.de/preprints”
A finite element method enriched for wave propagation problems (2012, background): “A considerable attention has been given to the development of discontinuous finite element formulations [41] [42] [43].”
hp analysis of a hybrid DG method for Stokes flow (2013, methodology): “This manuscript deals with the hp error analysis of a hybrid discontinuous Galerkin method for incompressible flow.”
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows (2013, unknown): “In particular, in contrast to the increasing stencil size needed to increase the accuracy of classical ﬁnite volume methods, the stencil of DGFEMs is the same for any order of accuracy, which has important advantages for the implementation of boundary conditions and for the parallel eﬃciency of the…”
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, background): “…it is then close to a particular case of the discontinuous Galerkin technique (Reed & Hill 1973; Arnold 1982; Falk & Richter 1999; Hu et al. 1999; Cockburn et al. 2000; Giraldo et al. 2002; Riviére & Wheeler 2003; Monk & Richter 2005; Grote et al. 2006; Ainsworth et al. 2006; Bernacki et al.…”
Machine learning in cardiovascular flows modeling: Predicting pulse wave propagation from non-invasive clinical measurements using physics-informed deep learning (2019, methodology): “el for the middle points of each domain and randomly selected values of t are presented in ﬁgure (5). Evidently, there is a good match between the solution acquired from Discontinuous Galerkin solver [9] and the one predicted by the proposed physic-informed neural networks model. The prediction erro”
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics (2010, background): “, the surveys [12,13,20], and the references therein.”
A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS (2009, methodology): “On the other hand, the 2p + 1 order uniform superconvergence of numerical fluxes are observed numerically for the LDG method under both the Shishkin and an improved grade meshes.”