Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

We introduce a physically relevant stochastic representation of the rotating shallow water
equations. The derivation relies mainly on a stochastic transport principle and on a …

We present a model-reduced variational Eulerian integrator for incompressible fluids, which
combines the efficiency gains of dimension reduction, the qualitative robustness of coarse …

We present a finite element variational integrator for compressible flows. The numerical
scheme is derived by discretizing, in a structure-preserving way, the Lie group formulation of …

We propose a finite-element discretization approach for the incompressible Euler equations
which mimics their geometric structure and their variational derivation. In particular, we …

Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of
dynamical systems deliver physically relevant results. In this paper, we construct a structure …

This paper presents a geometric variational discretization of compressible fluid dynamics.
The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie …

This article surveys research on the application of compatible finite element methods to
large-scale atmosphere and ocean simulation. Compatible finite element methods extend …

We present the material, spatial, and convective representations for elasticity and fluids with
a free boundary from the Lagrangian reduction point of view, using the material and spatial …

We develop a variational integrator for the shallow‐water equations on a rotating sphere.
The variational integrator is built around a discretization of the continuous Euler–Poincaré …