256 citations · 934 across the 55 of their papers we have counts for
14 papers · 1 filter
Numerical approximation of viscous contact problems applied to glacial sliding
Gonzalo G. de Diego, Patrick E. Farrell, Ian J. Hewitt
Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance i…
Transformations for Piola-mapped elements
Francis Aznaran, Robert Kirby, Patrick Farrell
The Arnold-Winther element successfully discretizes the Hellinger-Reissner variational formulation of linear elasticity; its development was one of the key early breakthroughs of t…
Variational and numerical analysis of a -tensor model for smectic-A liquid crystals
Jingmin Xia, Patrick E. Farrell
We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differenti…
Consolidated theory of fluid thermodiffusion
Alexander Van-Brunt, Patrick E. Farrell, Charles W. Monroe
We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinet…
On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
Gonzalo G. de Diego, Patrick E. Farrell, Ian J. Hewitt
Stokes variational inequalities arise in the formulation of glaciological problems involving contact. We consider the problem of a two-dimensional marine ice sheet with a grounding…
A scalable and robust vertex-star relaxation for high-order FEM
Pablo D. Brubeck, Patrick E. Farrell
Pavarino proved that the additive Schwarz method with vertex patches and a low-order coarse space gives a -robust solver for symmetric and coercive problems. However, for very h…