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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 Bochev +2 more
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The Hybridizable Discontinuous Galerkin Methods
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011We introduce the hybridizable discontinuous Galerkin (HDG) methods in the framework of steady-state diffusion problems and show why they can be implemented more efficiently than any other DG method and why they are also more accurate. We then give an overview of the application of these methods to several problems including wave propagation, linear and
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The Hybridizable Discontinuous Galerkin Method
2019In this section, we show how the spaces of RT and BDM can be balanced to have an equal polynomial degree. Stability will be restored using a discrete stabilization (not penalization) function. This is how local quantities of RT, BDM, and HDG methods compare.
Shukai Du, Francisco-Javier Sayas
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Introduction to Discontinuous Galerkin Methods
2017The purpose of this chapter is to present an overview of the construction of discontinuous Galerkin finite element methods for a general class of second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic partial differential equations, ultra-parabolic equations,
Andrea Cangiani +3 more
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The Discontinuous Galerkin Trefftz Method
2015In the following work we develop a novel numerical method, which is used to approximate time-dependent Maxwell's equations. The method combines an already existing discontinuous Galerkin (DG) method with polynomial Trefftz functions. These polynomial Trefftz functions exactly solve Maxwell's equations in an element-wise fashion.
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A contact-electro-catalytic cathode recycling method for spent lithium-ion batteries
Nature Energy, 2023, Andy Berbille, Wei Tang
exaly