In some previous works, the authors have introduced a strategy to develop well-balanced
high-order numerical methods for nonconservative hyperbolic systems in the framework of …

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 first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element
scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler …

We introduce a general framework for the construction of well-balanced finite volume
methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense …

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 propose a novel set of first-order hyperbolic equations that can model
dispersive non-hydrostatic free surface flows. The governing PDE system is obtained via a …

This paper presents a novel semi-implicit hybrid finite volume/finite element (FV/FE) scheme
for the numerical solution of the incompressible and weakly compressible Navier-Stokes …

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 …

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite
element scheme for the numerical solution of the incompressible viscous and resistive …