PUBLICATIONS & PREPRINTS

PAPERS

Date	Title	Co-authors
JAN.2025 (arXiv), APR.2026 (SISC)	Helicity-preserving finite element discretization for magnetic relaxation	Mingdong He, Patrick Farrell, Kaibo Hu
APR.2025 (arXiv), DEC.2025 (SISC)	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables	Patrick Farrell

PREPRINTS

(In review)

Date	Title	Co-authors
JUN.2026 (arXiv), In review (SISC)	Automated Galerkin time stepping in Irksome	Pablo Brubeck, Patrick Farrell, Rob Kirby, Scott MacLachlan

MAY.2026 (arXiv), In review (SISC)	Arbitrary-order structure-preserving discretizations for geometric curvature flows	Ganghui Zhang, Patrick Farrell
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
NOV.2025 (access)	Geometric numerical integration via auxiliary variables (PhD (DPhil) thesis)

IN PREPARATION

(Drafts available on request)

Title	Co-authors
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

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