We present a general family of subcell limiting strategies to construct robust high-order
accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct …

We present Trixi. jl, a Julia package for adaptive high-order numerical simulations of
hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi. jl is extensible, easy …

A theoretical analysis of the entropy conservation properties is conducted to explain the
different behaviors of the non-dissipative finite-difference spatial discretization schemes …

In this paper, we will build a roadmap for the growing literature of high order quadrature-
based entropy stable discontinuous Galerkin (DG) methods, trying to elucidate the …

This work examines the development of an entropy conservative (for smooth solutions) or
entropy stable (for discontinuous solutions) space–time discontinuous Galerkin (DG) method …

For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form
discontinuous Galerkin discretizations have robustness issues when trying to solve the …

One of the challenges when simulating astrophysical flows with self-gravity is to compute the
gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is …

We present a new class of efficient and robust discontinuous spectral-element methods of
arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular …

Recently, an approach known as relaxation has been developed for preserving the correct
evolution of a functional in the numerical solution of initial-value problems, using Runge …