It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy
cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and …

Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

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 …

This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and
finite volume methods which provably preserve the positivity of density and pressure for the …

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and
Navier-Stokes equations require the positivity of thermodynamic quantities in order to …

We consider a class of time-dependent second order partial differential equations governed
by a decaying entropy. The solution usually corresponds to a density distribution, hence …

We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for
solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes …

In the numerical simulation of ideal magnetohydrodynamics (MHD), keeping the pressure
and density always positive is essential for both physical considerations and numerical …

For time-dependent PDEs, the numerical schemes can be rendered bound-preserving
without losing conservation and accuracy by a postprocessing procedure of solving a …

In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …