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math.NA2026
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…
math.NA2026
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…
math.NA2026
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…