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Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon.
The calculation of the interaction of non-stationary shock waves and obstacles
V. V. Rusanov · 1962
Earlier work this paper cites.
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
G. A. Sod · 1978
Earlier work this paper cites.
First order quasilinear equations with boundary conditions
C. Bardos, A.-Y. LeRoux, and J.-C. Nédélec · 1979
Earlier work this paper cites.
Efficient implementation of essentially non-oscillatory shock-capturing schemes
C.-W. Shu and S. Osher · 1988
Earlier work this paper cites.
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems
B. Cockburn, S.-Y. Lin, and C.-W. Shu · 1989
Earlier work this paper cites.
Classification of the Riemann problem for two-dimensional gas dynamics
C. W. Schulz-Rinne · 1993
Earlier work this paper cites.
On the Gibbs phenomenon and its resolution
D. Gottlieb and C.-W. Shu · 1997
Earlier work this paper cites.
The Runge–Kutta discontinuous Galerkin method for conservation laws v: multidimensional systems
B. Cockburn and C.-W. Shu · 1998
Earlier work this paper cites.
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A. Burbeau, P. Sagaut, and C.-H. Bruneau · 2001
Earlier work this paper cites.
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D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini · 2002
Earlier work this paper cites.
Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
A. Kurganov and E. Tadmor · 2002
Earlier work this paper cites.
High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD
C.-W. Shu · 2003
Earlier work this paper cites.
Discontinuous Galerkin methods for first-order hyperbolic problems
F. Brezzi, L. D. Marini, and E. Süli · 2004
Earlier work this paper cites.
Hermite WENO schemes and their application as limiters for Runge–Kutta discontinuous Galerkin method: one-dimensional case
J. Qiu and C.-W. Shu · 2004
Earlier work this paper cites.
Hyperbolic conservation laws in continuum physics
C. M. Dafermos and C. M. Dafermos · 2005
Earlier work this paper cites.
Runge–Kutta discontinuous Galerkin method using WENO limiters
J. Qiu and C.-W. Shu · 2005
Earlier work this paper cites.
An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes—II. The three-dimensional isotropic case
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Earlier work this paper cites.
Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier–Stokes equations
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Earlier work this paper cites.
Sub-cell shock capturing for discontinuous Galerkin methods
P.-O. Persson and J. Peraire · 2006
Earlier work this paper cites.
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Earlier work this paper cites.
Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws
A. Kurganov, G. Petrova, and B. Popov · 2007
Earlier work this paper cites.
A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows
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Earlier work this paper cites.
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High-order discontinuous Galerkin discretization of transonic turbulent flows
F. Bassi, A. Crivellini, A. Ghidoni, and S. Rebay · 2009
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Nodal discontinuous Galerkin methods on graphics processors
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Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks
A. Mani, J. Larsson, and P. Moin · 2009
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P. Wesseling · 2009
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Decoupled weight decay regularization
I. Loshchilov and F. Hutter · 2017
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Automatic differentiation in Pytorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
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