9 papers
Accelerated implicitization: Robust fixed-point iterations arising from an explicit scheme
Nicolas A. Barnafi, Felipe Galarce, Pablo Brubeck
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence…
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…
Cohomology of Finite Element Stokes Complexes on Alfeld Splits
Pablo D. Brubeck, Yizhou Liang, Charles Parker
We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzmán, & Neilan (2020, Math. Comp., 8…
Achieving Material Robustness via Symmetric Stress Finite Element Discretizations
Pablo Brubeck, Charles Parker, Umberto Zerbinati
When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly…
Fast solvers for the high-order FEM simplicial de Rham complex: Extended edition
Pablo D. Brubeck, Patrick E. Farrell, Robert C. Kirby +1
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces…
DefElement: an encyclopedia of finite element definitions
Matthew W. Scroggs, Pablo D. Brubeck, Joseph P. Dean +2
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elemen…