Large-scale dynamics of the oceans and the atmosphere are governed by primitive
equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is …

The long-term success of climate models that operate on multiresolution grids depends on
access to subgrid parameterizations that act appropriately across a wide range of spatial …

As a model problem for the barotropic mode of the primitive equations of the oceans and
atmosphere, we consider the Euler system on a bounded convex planar domain Ω …

In this article we consider the inviscid two-dimensional shallow water equations in a
rectangle. The flow occurs near a stationary solution in the so called supercritical regime …

The aim of this article is to study a model of two superposed layers of fluid governed by the
shallow water equations in space dimension one. Under some suitable hypotheses the …

This review article concerns multi-level methods for finite volume discretizations. They are
presented in the context of the non-viscous shallow water equations in space dimension one …

A general framework for goal-oriented a posteriori error estimation for finite volume methods
is developed. The framework does not rely on recasting finite volume methods as special …

The authors consider a simple transport equation in one-dimensional space and the
linearized shallow water equations in two-dimensional space, and describe and implement …

New avenues are explored for the numerical study of the two dimensional inviscid
hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence …

We construct the cell-centered Finite Volume discretization of the two-dimensional inviscid
primitive equations in a domain with topography. To compute the numerical fluxes, the so …