525 citations · 1.2k across the 24 of their papers we have counts for
24 papers
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…
An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers
Fabian Laakmann, Patrick E. Farrell, Lawrence Mitchell
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the elect…
Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
Justin Crum, Cyrus Cheng, David A. Ham +4
We present an implementation of the trimmed serendipity finite element family, using the open source finite element package Firedrake. The new elements can be used seamlessly withi…
A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott +1
Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust preconditioners for the stationary incompressible Navier-Stokes equations, but only for specific disc…
Robust multigrid methods for nearly incompressible elasticity using macro elements
Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott +1
We present a mesh-independent and parameter-robust multigrid solver for the Scott-Vogelius discretisation of the nearly incompressible linear elasticity equations on meshes with a…
PCPATCH: software for the topological construction of multigrid relaxation methods
Patrick E. Farrell, Matthew G. Knepley, Lawrence Mitchell +1
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß-Seidel are inadequate, and more sophisticated space decompos…