91 citations · 246 across the 6 of their papers we have counts for
8 papers
Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties
Abner J. Salgado, Ignacio Tomas
We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions…
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
Yimin Lin, Jesse Chan, Ignacio Tomas
High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guara…
Thermodynamically consistent physics-informed neural networks for hyperbolic systems
Ravi G. Patel, Indu Manickam, Nathaniel A. Trask +4
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the P…
Second-order invariant domain preserving approximation of the compressible Navier--Stokes equations
Jean-Luc Guermond, Matthias Maier, Bojan Popov +1
We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to b…
Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
Jean-Luc Guermond, Bojan Popov, Ignacio Tomas
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided element…
Second-order invariant domain preserving approximation of the Euler equations using convex limiting
Jean-Luc Guermond, Murtazo Nazarov, Bojan Popov +1
A new second-order method for approximating the compressible Euler equations is introduced. The method preserves all the known invariant domains of the Euler system: positivity of…