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A Multiscale Discontinuous Galerkin Method
2006We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components.
Pavel B. Bochev +2 more
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Discontinuous Galerkin Methods
2016The discontinuous Galerkin (dG) method was introduced by Reed and Hill [73] in 1973 for steady-state neutron transport as an hyperbolic problem. This was followed by other studies; by Bassi and Rebay [12] for the compressible Navier-Stokes equations, Cockburn and Shu [31] developed the local discontinuous Galerkin (ldG) method for advection-diffusion ...
Gary Cohen, Sébastien Pernet
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Discontinuous Galerkin and Related Methods for ODE
Journal of Scientific Computing, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discontinuous Galerkin Methods
2012In this final chapter we present the discontinuous Galerkin (dG) method. This method is based on finite element spaces that consist of discontinuous piecewise polynomials defined on a partition of the computational domain. Such methods are very flexible, for example, since they allow construction of more general methods and since they allow for simple ...
Mats G. Larson, Fredrik Bengzon
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Discontinuous Galerkin Methods
2008In this article, we describe some simple and commonly used discontinuous Galerkin methods for elliptic, Stokes and convection-diffusion problems. We illustrate these methods by numerical experiments.
Vivette Girault, Mary F. Wheeler
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Discontinuous Galerkin in time
2021In the previous two chapters, we have used finite differences to approximate the time derivative in the space semi-discrete parabolic problem. We now adopt a different viewpoint directly relying on a space-time weak formulation. The time approximation is realized by using piecewise polynomial functions over the time mesh.
Alexandre Ern, Jean-Luc Guermond
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On discontinuous Galerkin methods
International Journal for Numerical Methods in Engineering, 2003AbstractDiscontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present. Several alternatives for treating the diffusion and advective fluxes have been introduced. This report summarizes some of the methods that have been proposed.Several numerical examples are included
Zienkiewicz, OC +3 more
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Discontinuous Galerkin Methods in Nanophotonics
Advanced Photonics Congress, 2012A review of the current status of Discontinuous Galerkin methods and their applications in nano-photonics is provided and future directions in methodic developments and applications are discussed.
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Discontinuous Galerkin Methods
2018Two GDMs are obtained from the Discontinuous Galerkin setting. The first one recovers the high order SIPG schemes in the case of linear problems, the second one, based on average jumps, leads to simpler computations.
Jérôme Droniou +4 more
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