PUBLICATIONS & PREPRINTS

PAPERS

Date	Title	Co-authors
29.APR.2025 (arXiv), 31.DEC.2025 (SISC)	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables	Patrick Farrell

(Upcoming)

Date	Title	Co-authors
20.JAN.2025 (arXiv), 30.APR.2026 (SISC)	Helicity-preserving finite element discretization for magnetic relaxation	Mingdong He, Patrick Farrell, Kaibo Hu

PREPRINTS

(In review)

Date	Title	Co-authors
28.NOV.2025 (arXiv), In review (CAMWA)	Conservative and dissipative discretisations of multi-conservative ODEs and GENERIC systems	Patrick Farrell

OTHER WORKS

Date	Title	Co-authors
02.NOV.2025 (access)	Geometric numerical integration via auxiliary variables (PhD (DPhil) thesis)

IN PREPARATION

(Drafts available on request)

Title	Co-authors
Automated Galerkin time stepping in Irksome	Pablo Brubeck, Colin Cotter, Patrick Farrell, Rob Kirby, Scott MacLachlan
Enstrophy-stable integrators for the incompressible Navier–Stokes equations	Matin Shams, Patrick Farrell
Energy-stable discretisations of viscoelastic flows	Dennis Trautwein, Patrick Farrell
Energy- and entropy-stable discretisations for the quasi-incompressible Maxwell–Stefan equations	Aaron Brunk, Patrick Farrell, Mária Lukácová-Medviďová
Conservative and accurately dissipative finite element integrators for geometric PDEs	Ganghui Zhang, Patrick Farrell

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