For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian
(ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of …

This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin
schemes with subcell finite volume limiters applied to a new class of first order hyperbolic …

In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of
the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear …

Abstract ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving
systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are …

In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

We propose a new arbitrary high order accurate semi-implicit space–time discontinuous
Galerkin (DG) method for the solution of the two and three dimensional compressible Euler …

In this paper we propose a new reformulation of the first order hyperbolic model for unsteady
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …