Error estimation and control are critical ingredients for improving the reliability of
computational simulations. Adjoint-based techniques can be used to both estimate the error …

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

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

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 …

We describe a limiter for the discontinuous Galerkin method that retains as high an order as
possible, and does not automatically reduce to first order. The limiter is a generalization 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 …

Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element
discretization to resolve a shock layer within a single cell. However, when a non-smooth …

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 …

We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …