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Discontinuous Galerkin methods in nanophotonics [PDF]
Laser & Photonics Reviews, 2011 AbstractThis article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities.
Busch, K., König, M., Niegemann, J.
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Convergence of adaptive discontinuous Galerkin methods [PDF]
Mathematics of Computation, 2018 We develop a general convergence theory for adaptive discontinu- ous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically relevant marking strategies. Another key feature of the presented result is, that it holds for penalty parameters only necessary for the standard analysis of the respective ...
Kreuzer, Christian +1 more
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Advances in Mathematical Physics, 2017 We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes
Meilan Qiu, Liquan Mei, Dewang Li
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An Introduction to the Hybridizable Discontinuous Galerkin Method [PDF]
, 2021 The final publication is available at link.springer.com This chapter in intended to be a didactical introduction to the Hybridizable Discontinuous Galerkin (HDG) method, including the formulation and its implementation. The Laplace and Stokes equations are considered as representative problems with self-adjoint operators, accounting for the ...
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High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation [PDF]
, 2018 We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time.
Coulette, David +4 more
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Journal of Inequalities and Applications, 2010 We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Hyun Young Lee +2 more
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Mathematical Modelling and Analysis, 2012 In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation.
Zongxiu Ren +3 more
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Numerical analysis of the neutron multigroup $SP_N$ equations
Comptes Rendus. Mathématique, 2021 The multigroup neutron $SP_N$ equations, which are an approximation of the neutron transport equation, are used to model nuclear reactor cores. In their steady state, these equations can be written as a source problem or an eigenvalue problem.
Jamelot, Erell, Madiot, François
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Discontinuous Galerkin methods for the biharmonic problem [PDF]
IMA Journal of Numerical Analysis, 2008 This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal.
Georgoulis, EH, Houston, P
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SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics [PDF]
, 2017 We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as
Bohn, Andy +13 more
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