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Discontinuous Galerkin Methods [PDF]
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2000 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.
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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 ...
Carstensen, C. +3 more
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Advances in Mechanical Engineering, 2019 In this work, we deal with high-order solver for incompressible flow based on velocity correction scheme with discontinuous Galerkin discretized velocity and standard continuous approximated pressure.
Liyang Xu +5 more
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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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ADER discontinuous Galerkin Material Point Method
International Journal for Numerical Methods in Engineering, 2023 AbstractThe first‐order accurate discontinuous Galerkin Material Point Method (DGMPM), initially introduced by Renaud et al. (J Comput Phys. 2018;369:80–102.), considers a solid body discretized by a collection of material points carrying the history of the matter, embedded in an arbitrary grid on which a nodal discontinuous Galerkin approximation is ...
Alaa Lakiss +3 more
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An analytical and numerical approach for the $(1+1)$-dimensional nonlinear Kolmogorov–Petrovskii–Piskunov equation [PDF]
Iranian Journal of Numerical Analysis and OptimizationThe main focus of this work is to develop and implement an efficient lo-cal discontinuous Galerkin scheme for acquiring the numerical solution of the (1 + 1)-dimensional nonlinear Kolmogorov–Petrovskii–Piskunov equa-tion. The proposed framework employs a
A. Chand, J. Mohapatra
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Discontinuous Galerkin method on reference domain
Computer Assisted Methods in Engineering and Science, 2017 A reference domain is chosen to formulate numerical model using the discontinuous Galerkin with finite difference (DGFD) method. The differential problem, which is defined for the real domain, is transformed in a weak form to the reference domain.
Jan Jaśkowiec
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Space-time discontinuous Galerkin method for the numerical simulation of the compressible turbulent gas flow through the porous media [PDF]
EPJ Web of Conferences, 2019 The article is concerned with the numerical simulation of the compressible turbulent gas flow through the porous media using space-time discontinuous Galerkin method.The mathematical model of flow is represented by the system of non-stationary Reynolds ...
Česenek Jan
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Pointwise best approximation results for Galerkin finite element solutions of parabolic problems [PDF]
, 2016 In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm.
Leykekhman, Dmitriy, Vexler, Boris
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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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