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Discontinuous Galerkin methods [PDF]
ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2003 AbstractThis paper is a short essay on discontinuous Galerkin methods intended for a very wide audience. We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block‐diagonal.
Bernardo Cockburn
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Resolving phase transitions with discontinuous Galerkin methods
SciPost Physics Core, 2023 We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (fRG). We investigate the $O(N)$-model in the large $N$ limit.
Eduardo Grossi, Nicolas Wink
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Journal of Harbin University of Science and Technology, 2022 The equivalence between direct flux reconstruction method and discontinuous Galerkin method for solving parabolic equation and convection-diffusion equation is studied.
BI Hui, LIU Lei
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A multilevel discontinuous Galerkin method [PDF]
Numerische Mathematik, 2003 With extended references to the major papers on the subject, this work analyzes mathematically multigrid techniques for two discontinuous Galerkin methods: one for elliptic problems and a second one for singular perturbed advection-diffusion problems. In the former case, the analysis predicts convergence rates of the multigrid method independent of the
Jay Gopalakrishnan, Guido Kanschat
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Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup
Computation, 2021 This paper presents a new depth-integrated non-hydrostatic finite element model for simulating wave propagation, breaking and runup using a combination of discontinuous and continuous Galerkin methods.
Lucas Calvo +3 more
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Nonlinear discontinuous Petrov–Galerkin methods [PDF]
Numerische Mathematik, 2018 The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a reduced formulation, and a weighted nonlinear least ...
Carsten Carstensen +3 more
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Convergence of a Discontinuous Galerkin Multiscale Method [PDF]
SIAM Journal on Numerical Analysis, 2013 A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(Ω,\mathbb{R}^{d\times d}_{sym})$ with uniform spectral bounds and without any assumption on scale separation or periodicity.
Daniel Elfverson +3 more
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Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods
Applied and Computational Mechanics, 2022 The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely ...
Levý T., May G.
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Multisymplecticity of Hybridizable Discontinuous Galerkin Methods [PDF]
Foundations of Computational Mathematics, 2019 In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential equations. We show that these conditions are satisfied by the "hybridized" versions of several of the most commonly-used ...
Robert I. McLachlan, Ari Stern
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Numerical approximation of time-fractional Burgers-type equation
Advances in Difference Equations, 2020 In this work, we analyze and test a local discontinuous Galerkin method for solving the Burgers-type equation. The proposed numerical method, which is high-order accurate, is based on a finite difference scheme in time and local discontinuous Galerkin ...
Miaomiao Yang
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