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 …

Recent work on solving partial differential equations (PDEs) with deep neural networks
(DNNs) is presented. The paper reviews and extends some of these methods while carefully …

Recent work has introduced a simple numerical method for solving partial differential
equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the …

This work extends the flux-corrected transport (FCT) methodology to arbitrary order
continuous finite element discretizations of scalar conservation laws on simplex meshes …

The use of high‐order polynomials in discontinuous Galerkin (DG) approximations to
convection‐dominated transport problems tends to cause a violation of the maximum …

In this paper, we present a collection of algorithmic tools for constraining high-order
discontinuous Galerkin (DG) approximations to hyperbolic conservation laws. We begin with …

Many mathematical models of computational fluid dynamics involve transport of conserved
quantities, which must lie in a certain range to be physically meaningful. The analytical or …

Schemes for the incompressible Navier–Stokes and Boussinesq equations are formulated
and derived combining the novel Hybridizable Discontinuous Galerkin (HDG) method, a …

We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow
water equations based on a computationally efficient adaptivity indicator which works …

In the modelling of hydrodynamics, the Discontinuous Galerkin (DG) approach constitutes a
more complex and modern alternative to the well-established finite volume method. The …