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Discontinuous Galerkin methods [PDF]
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für 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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On discontinuous Galerkin methods [PDF]
International Journal for Numerical Methods in Engineering, 2003 AbstractDiscontinuous 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
O.C. Zienkiewicz +3 more
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Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions [PDF]
SIAM Journal on Numerical Analysis, 2005 The author proves convergence of a discontinuous Galerkin method for a convection-reaction equation under very weak assumptions on the coefficients. The proof is based on work of \textit{R. J. DiPerna} and \textit{P. L. Lions} [Invent. Math. 98, 511--547 (1989; Zbl 0696.34049)]. Applications include modeling the flow of incompressible immiscible fluids.
Noel J. Walkington
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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
Gopalakrishnan, Jay, Kanschat, Guido
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Axioms, 2023 For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points.
Omar A. Khalil, Gerd Baumann
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A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics [PDF]
SIAM Journal on Scientific Computing, 2018 The density and pressure are positive physical quantities in magnetohydrodynamics (MHD). Design of provably positivity-preserving (PP) numerical schemes for ideal compressible MHD is highly desirable but remains a challenge, especially in the ...
Kailiang Wu, Chi-Wang Shu
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Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov–Poisson System [PDF]
Communication on Applied Mathematics and Computation, 2020 We propose a class of conservative discontinuous Galerkin methods for the Vlasov–Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable.
F. Filbet, T. Xiong
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A superconvergent hybridisable discontinuous Galerkin method for linear elasticity [PDF]
International Journal for Numerical Methods in Engineering, 2018 The first superconvergent hybridisable discontinuous Galerkin method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented.
R. Sevilla +3 more
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Numerical analysis of variable-order fractional KdV-Burgers-Kuramoto equation
Electronic Research Archive, 2022 In this paper, a fully discrete local discontinuous Galerkin finite element method is proposed to solve the KdV-Burgers-Kuramoto equation with variable-order Riemann-Liouville time fractional derivative.
Leilei Wei , Xiaojing Wei, Bo Tang
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