In this work we present a framework for enforcing discrete maximum principles in
discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to …

Numerical schemes provably preserving the positivity of density and pressure are highly
desirable for ideal magnetohydrodynamics (MHD), but the rigorous positivity-preserving …

We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous
Galerkin spectral-element methods (DGSEMS). The use of Legendre-Gauss-Lobatto (LGL) …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

Many mathematical models of computational fluid dynamics involve transport of conserved
quantities, which must lie in a certain range to be physically meaningful. The analytical or …

In this paper, we use an implicit two-derivative deferred correction time discretization
approach and combine it with a spatial discretization of the discontinuous Galerkin spectral …

In this work, we discuss and develop multidimensional limiting techniques for discontinuous
Galerkin (DG) discretizations of scalar hyperbolic problems. To ensure that each cell …

The methodology proposed in this paper bridges the gap between entropy stable and
positivity-preserving discontinuous Galerkin (DG) methods for nonlinear hyperbolic …

There have been intensive studies on maximum-principle-satisfying and positivity-
preserving methods for hyperbolic conservation laws. Most of them are based on the method …

Second and higher order numerical approximations of conservation laws for vector fields
call for the use of limiting techniques based on generalized monotonicity criteria. In this …