Approximation rate bounds for emulations of real-valued functions on intervals by deep
neural networks (DNNs) are established. The approximation results are given for DNNs …

In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …

In rivers, coastal seas and transitional waters, sediment transport processes involve a variety
of interacting factors that dynamically vary over time and space. The flow dynamics within …

We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …

This review paper describes a class of scheme named “residual distribution schemes” or
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …

For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

We describe and review non oscillatory residual distribution schemes that are rather natural
extension of high order finite volume schemes when a special emphasis is put on the …

In the hyperbolic research community, there exists the strong belief that a continuous
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …

This paper proposes an invariant-domain preserving approximation technique for nonlinear
conservation systems that is high-order accurate in space and time. The algorithm mixes a …

This paper presents a semi-Lagrangian meshless framework based on the localized radial
basis function collocation method and the second-order explicit Runge–Kutta method (RK2 …