5 papers
Automated Galerkin time stepping in Irksome
Boris D. Andrews, Pablo Brubeck, Patrick E. Farrell +2
As the study of temporal and spatial discretization schemes continues to advance, recent work has focused on the use of Galerkin-in-time discretization schemes that enable broader…
Arbitrary-order structure-preserving discretizations for geometric curvature flows
Ganghui Zhang, Boris D. Andrews, Patrick E. Farrell
Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surfac…
Conservative and dissipative discretisations of multi-conservative ODEs and GENERIC systems
Boris D. Andrews, Patrick E. Farrell
Ordinary and partial differential equations describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated qu…
Helicity-preserving finite element discretization for magnetic relaxation
Mingdong He, Patrick E. Farrell, Kaibo Hu +1
The Parker conjecture, which explores whether magnetic fields in perfectly conducting plasmas can develop tangential discontinuities during magnetic relaxation, remains an open que…
Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables
Boris D. Andrews, Patrick E. Farrell
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represen…