PUBLICATIONS & PREPRINTS

Preprints

(Accepted for publication)

Date	Title	Co-authors
29.APR.2025 (arXiv), Upcoming (SISC)	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables	Patrick Farrell

(In review)

Date	Title	Co-authors
20.JAN.2025 (arXiv)	Helicity-preserving finite element discretization for magnetic relaxation	Mingdong He, Patrick Farrell, Kaibo Hu

OTHER WORKS

Date	Title	Co-authors
18.JUL.2025 (download)	Geometric numerical integration via auxiliary variables (PhD (DPhil) thesis)
16.JUL.2024 (arXiv)	High-order conservative and accurately dissipative numerical integrators via auxiliary variables	Patrick Farrell

IN PREPARATION

(Drafts available on request)

Title	Co-authors
Conservative and dissipative time discretisations for conservative and GENERIC systems	Patrick Farrell
Automated Galerkin time stepping in Irksome	Pablo Brubeck, Patrick Farrell, Rob Kirby, Scott MacLachlan
Enstrophy-stable integrators for the incompressible Navier–Stokes equations	Matin Shams
An augmented Lagrangian preconditioner for natural convection at high Reynolds number	Alexei Gazca, Patrick Farrell
Uniformly accurate asymptotic-preserving integrators for charged particles

(Drafts not yet available)

Title	Co-authors
Helicity- and enstrophy-stable integrators for the Navier–Stokes–Voigt equations
Globally and locally structure-preserving mixed finite element methods for boundary-value problems
Enstrophy-stable integrators for the Navier–Stokes equations on manifolds
Enstrophy-stable integrators for incompressible magneto-hydrodynamics

(Click titles for further details, open problems, talks and more)