256 citations · 934 across the 55 of their papers we have counts for
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Structural electroneutrality in Onsager-Stefan-Maxwell transport with charged species
Alexander Van-Brunt, Patrick E. Farrell, Charles W. Monroe
We present a method to embed local electroneutrality within Onsager-Stefan-Maxwell electrolytic-transport models, circumventing their formulation as differential systems with an al…
Multigrid solvers for the de Rham complex with optimal complexity in polynomial degree
Pablo D. Brubeck, Patrick E. Farrell
The Riesz maps of the de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multi…
Two conjectures on the Stokes complex in three dimensions on Freudenthal meshes
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are…
Finite element methods for multicomponent convection-diffusion
Francis R. A. Aznaran, Patrick E. Farrell, Charles W. Monroe +1
We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low…
Finite-element discretization of the smectic density equation
Patrick E. Farrell, Abdalaziz Hamdan, Scott P. MacLachlan
The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators…
Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations
Fabian Laakmann, Patrick E. Farrell, Kaibo Hu
We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current ter…