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 book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase,
global models are moving towards fully nonhydrostatic dynamical cores, with the local and …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

High order methods based on diagonal-norm summation by parts operators can be shown
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …

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 consider edge‐based reconstruction (EBR) schemes for solving the Euler
equations on unstructured tetrahedral meshes. These schemes are based on a high …

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 …

A new approach to slope limiting for discontinuous Galerkin methods on arbitrary meshes is
introduced. A local Taylor basis is employed to express the approximate solution in terms of …

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 …