89 citations · 223 across the 9 of their papers we have counts for
11 papers
First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system
Jean-Luc Guermond, Matthias Maier, Bojan Popov +2
The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to…
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
Bennett Clayton, Jean-Luc Guermond, Matthias Maier +2
This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation techniq…
On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations
Jean-Luc Guermond, Martin Kronbichler, Matthias Maier +2
This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excell…
Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography
Jean-Luc Guermond, Chris Kees, Bojan Popov +1
The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as the fully non-linear Boussinesq equations…
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…
Positive asymptotic preserving approximation of the radiation transport equation
Jean-Luc Guermond, Bojan Popov, Jean Ragusa
We introduce a (linear) positive and asymptotic preserving method or solving the one-group radiation transport equation. The approximation in space is discretization agnostic: the…
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…
Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations
Jean-Luc Guermond, Bojan Popov
This paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the Riemann solution for the Euler system of gas dynamics with t…
Invariant domains and first-order continuous finite element approximation for hyperbolic systems
Jean-Luc Guermond, Bojan Popov
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The…
Viscous regularization of the Euler equations and entropy principles
Jean-Luc Guermond, Bojan Popov
This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the genera…