This review paper concerns the application of numerical methods of the Godunov type to the
computation of approximate solutions to free-surface gravity flows modelled under a shallow …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

In this article, a conservative least-squares polynomial reconstruction operator is applied to
the discontinuous Galerkin method. In a first instance, piecewise polynomials of degree N …

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 …

The present paper introduces a class of finite volume schemes of increasing order of
accuracy in space and time for hyperbolic systems that are in conservation form. The …

In this paper we develop a novel two-stage fourth order time-accurate discretization for time-
dependent flow problems, particularly for hyperbolic conservation laws. Different from the …

We study weno (2r− 1) reconstruction [DS Balsara, CW Shu, Monotonicity prserving weno
schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452] …

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 …

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 …