412 citations · 1.7k across the 26 of their papers we have counts for
28 papers
Local -bounded commuting projections in FEEC
Douglas N. Arnold, Johnny Gúzman
We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in and commute with the…
The landscape law for tight binding Hamiltonians
Douglas N. Arnold, Marcel Filoche, Svitlana Mayboroda +2
The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schrödinger operator on . In particular, we establish upper and lower bound…
Sharp estimates for the integrated density of states in Anderson tight-binding models
Perceval Desforges, Svitlana Mayboroda, Shiwen Zhang +4
Recent work [G. David, M. Filoche, and S. Mayboroda, arXiv:1909.10558[Adv. Math. (to be published)]] has proved the existence of bounds from above and below for the Integrated Dens…
Complexes from complexes
Douglas N. Arnold, Kaibo Hu
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum me…
The Hellan-Herrmann-Johnson method with curved elements
Douglas N. Arnold, Shawn W. Walker
We study the finite element approximation of the Kirchhoff plate equation on domains with curved boundaries using the Hellan-Herrmann-Johnson (HHJ) method. We prove optimal converg…
Localization of eigenfunctions via an effective potential
Douglas N. Arnold, Guy David, Marcel Filoche +2
We consider the localization of eigenfunctions for the operator $L=-\mbox{div} A \nabla + V$ on a Lipschitz domain and, more generally, on manifolds with and without boundary.…