Electronic Journal of Differential Equations, 2016 The goal of this article is to explore and motivate stabilization requirements for various types of discontinuous Galerkin (DG) methods. A new approach for the understanding of DG approximation methods for second order elliptic partial differential ...
Thomas Lewis
doaj
International Journal for Numerical Methods in Engineering, Volume 126, Issue 24, 30 December 2025.ABSTRACT Fast and efficient simulation strategies are a basic requirement of technologies such as digital twins. Particularly for roadway infrastructure, recent developments have demonstrated that the arbitrary Lagrangian Eulerian (ALE) formulation can be utilized to improve computational efficiency, when simulating the response of such pavement ...
Atul Anantheswar +5 more
wiley +1 more source
A highly accurate discontinuous Galerkin method for solving nonlinear Bratu's problem
Alexandria Engineering JournalIn this manuscript, we present an innovative approach to address nonlinear Bratu's problem by applying the Discontinuous Galerkin method. Our method accurately computes two-branched numerical solutions of the problem.
H. Temimi, M. Ben-Romdhane
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Preconditioning GMRES for discontinuous Galerkin approximations
Computer Assisted Methods in Engineering and Science, 2023 The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems.
Krzysztof Banaś, Mary F. Wheeler
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Discontinuous Galerkin finite element approximation of non-divergence form elliptic equations with Cordes coefficients [PDF]
, 2012 Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods.
Smears, Iain, Suli, Endre
core
A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems. [PDF]
Sci Rep, 2023 Jaśkowiec J, Pamin J.
europepmc +1 more source
The Dual Characteristic-Galerkin Method
Comptes Rendus. MathématiqueThe Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM)
Hecht, Frédéric, Pironneau, Olivier
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Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method. [PDF]
Int J Numer Methods Eng, 2022 Romor F, Tezzele M, Lario A, Rozza G.
europepmc +1 more source
Error analysis of a continuous-discontinuous Galerkin finite element method for generalized 2D vorticity dynamics [PDF]
, 2005 A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite element method suitable for two-dimensional geophysical flows.
Bokhove, O. +2 more
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Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations [PDF]
, 2009 The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical
Atkins, Harold L.
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