94 citations · 196 across the 20 of their papers we have counts for
17 papers · 1 filter
Learning robust marking policies for adaptive mesh refinement
Andrew Gillette, Brendan Keith, Socratis Petrides
In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a naïve marking policy leads to inefficient use of…
The Delaunay Density Diagnostic
Andrew Gillette, Eugene Kur
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs…
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…
Extending discrete exterior calculus to a fractional derivative
Justin Crum, Joshua A. Levine, Andrew Gillette
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerica…
Computational Serendipity and Tensor Product Finite Element Differential Forms
Andrew Gillette, Tyler Kloefkorn, Victoria Sanders
Many conforming finite elements on squares and cubes are elegantly classified into families by the language of finite element exterior calculus and presented in the Periodic Table…
Nonstandard finite element de Rham complexes on cubical meshes
Andrew Gillette, Kaibo Hu, Shuo Zhang
We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods…