[1]

R. Becker. Stoßwelle und detonation. Zeitschrift fur Physik, 8(1):321–362, 1922.

[2]

Bennett Clayton, Jean-Luc Guermond, and Bojan Popov. Invariant domain-preserving approximations for the Euler equations with tabulated equation of state. SIAM Journal on Scientific Computing, 44(1):A444–A470, 2022.

[3]

Bennett Clayton, Jean-Luc Guermond, Matthias Maier, Bojan Popov, and Eric J. Tovar. Robust second-order approximation of the compressible euler equations with an arbitrary equation of state. Journal of Computational Physics, page 111926, 2023.

[4]

Olivier Delestre, Carine Lucas, Pierre-Antoine Ksinant, Frédéric Darboux, Christian Laguerre, T-N-Tuoi Vo, Francois James, and Stéphane Cordier. Swashes: a compilation of shallow water analytic solutions for hydraulic and environmental studies. International Journal for Numerical Methods in Fluids, 72(3):269–300, 2013.

[5]

Jean-Luc Guermond and Bojan Popov. Fast estimation of the maximum wave speed in the riemann problem for the euler equations. Journal of Computational Physics, 321:908–926, 2016.

[6]

Jean-Luc Guermond and Bojan Popov. Invariant domains and first-order continuous finite element approximation for hyperbolic systems. SIAM Journal on Numerical Analysis, 54(4):2466–2489, 2016.

[7]

Jean-Luc Guermond, Matthias Maier, Bojan Popov, Laura Saavedra, and Ignacio Tomas. Greedy invariant-domain preserving approximation for hyperbolic systems. In preparation.

[8]

Jean-Luc Guermond, Richard Pasquetti, and Bojan Popov. Entropy viscosity method for nonlinear conservation laws. Journal of Computational Physics, 230(11):4248–4267, 2011.

[9]

Jean-Luc Guermond, Manuel Quezada de Luna, Bojan Popov, Christopher E. Kees, and Matthew W. Farthing. Well-balanced second-order finite element approximation of the shallow water equations with friction. SIAM Journal on Scientific Computing, 40(6):A3873–A3901, 2018.

[10]

Jean-Luc Guermond, Murtazo Nazarov, Bojan Popov, and Ignacio Tomas. Second-order invariant domain preserving approximation of the Euler equations using convex limiting. SIAM Journal on Scientific Computing, 40(5):A3211–A3239, 2018.

[11]

Jean-Luc Guermond, Matthias Maier, Bojan Popov, and Ignacio Tomas. Second-order invariant domain preserving approximation of the compressible navier–stokes equations. Computer Methods in Applied Mechanics and Engineering, 375(1):113608,

[12]

Jean-Luc Guermond, Martin Kronbichler, Matthias Maier, Bojan Popov, and Ignacio Tomas. On the implementation of a robust and efficient finite element-based parallel solver for the compressible navier-stokes equations. Computer Methods in Applied Mechanics and Engineering, 389:114250, 2022.

[13]

Matthias Maier and Martin Kronbichler. Efficient parallel 3d computation of the compressible euler equations with an invariant-domain preserving second-order finite-element scheme. ACM Transactions on Parallel Computing, 8(3):16:1–30, 2021.

[14]

S. Martínez-Aranda, J. Fernández-Pato, D. Caviedes-Voullième, I. García-Palacín, and P. García-Navarro.

[15]

W.F. Noh. Errors for calculations of strong shocks using an artificial viscosity and an artifiscial heat flux. Journal of Computational Physics, 72(1):78–120, 1987.

[16]

Mario Ricchiuto and Andreas Bollermann. Stabilized residual distribution for shallow water simulations. J. Comput. Phys., 228(4):1071–1115, 2009.

[17]

P. Woodward and P. Colella. The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 54:115–173, 1984.

[18]

Xiangxiong Zhang and Chi-Wang Shu. On positivity-preserving high order discontinuous galerkin schemes for compressible euler equations on rectangular meshes. Journal of Computational Physics, 229(23):8918–8934, 2010.