265 citations · 601 across the 26 of their papers we have counts for
5 papers · 1 filter
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…
Full waveform inversion using triangular waveform adapted meshes
Keith J. Roberts, Alexandre Olender, Lucas Franceschini +3
In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detaile…
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…
Additive Schwarz methods for serendipity elements
Jorge Marchena-Menendez, Robert C. Kirby
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensor-prod…
Bounds-constrained polynomial approximation using the Bernstein basis
Larry Allen, Robert C. Kirby
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforc…