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

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …

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] …

In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG)
finite element method on space–time adaptive Cartesian meshes (AMR) for 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 …

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …

We present a new class of high-order accurate numerical algorithms for solving the
equations of general-relativistic ideal magnetohydrodynamics in curved space–times. In this …

In this paper we discuss a new and very efficient implementation of high order accurate
arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite …