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The discontinuous Petrov–Galerkin method
Acta NumericaThe discontinuous Petrov–Galerkin (DPG) method is a Petrov–Galerkin finite element method with test functions designed for obtaining stability. These test functions are computable locally, element by element, and are motivated by optimal test functions which attain the supremum in an inf-sup condition.
Leszek Demkowicz, Jay Gopalakrishnan
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On discontinuous Galerkin methods
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
Zienkiewicz, OC +3 more
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International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 448-468, April 2026.The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault +6 more
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International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 492-509, April 2026.This paper presents a finite element method for simulating highly viscoelastic flows of pure polymer melts using the Elastic Viscous Stress Splitting formulation. The method avoids higher‐order derivatives in the weak formulation by reformulating the convective term in the constitutive equation.
R. Ahmad, P. Zajac, S. Turek
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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.
Lee HyunYoung, Shin JunYong, Ohm MiRay
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Comparison of DDFV and DG Methods for Flow in Anisotropic Heterogeneous Porous Media
Oil & Gas Science and Technology, 2014 We present a preliminary work to simulate gas injection in deep aquifers. Unsteady single-phase flows are considered. We compare Discrete Duality Finite Volume (DDFV, Discrete Duality Finite Volume) and Discontinuous Galerkin (DG, Discontinuous Galerkin)
Baron V., Coudière Y., Sochala P.
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مجلة المختار للعلوم, 2017 The volume integral of Riemann flux in the discontinuous Galerkin (DG) method is introduced in this paper. The boundaries integrals of the fluxes (Riemann flux) are transformed into volume integral.
Ibrahim. M. Rustum, ElHadi. I. Elhadi
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Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations on deforming meshes [PDF]
, 2006 An overview is given of a space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations. This method is well suited for problems with moving (free) boundaries which require the use of deforming elements. In addition,
Bos, F. van der +3 more
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, 2018 We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations.
Rhebergen, Sander, Wells, Garth N.
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A Parallelized 3D Geomechanical Solver for Fluid‐Induced Fault Slip in Poroelastic Media
International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 5, Page 2570-2586, 10 April 2026.ABSTRACT We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of CO2$\textrm {CO}_2$ storage. Utilizing a Galerkin finite‐element approach, both flow and poroelasticity equations are discretized on a shared three‐dimensional mesh.
Emil Rinatovich Gallyamov +4 more
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