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 …

There is strong observational evidence that the convective cores of intermediate-mass and
massive main sequence stars are substantially larger than those predicted by standard …

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 …

Convection is one of the most important mixing processes in stellar interiors. Hydrodynamic
mass entrainment can bring fresh fuel from neighboring stable layers into a convection zone …

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …

High-order Godunov methods for gas dynamics have become a standard tool for simulating
different classes of astrophysical flows. Their accuracy is mostly determined by the spatial …

We present a novel formulation of the discontinuous Galerkin spectral element method for
solving balance laws, with application to the shallow water equations. The scheme …

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 …

In the context of preserving stationary states, eg lake at rest and moving equilibria, a new
formulation of the shallow water system, called flux globalization has been introduced by …