photo of D. Arnold

Douglas N. Arnold

McKnight Presidential Professor of Mathematics
School of Mathematics, University of Minnesota

I am a mathematician and an educator. My research mostly concerns numerical analysis, partial differential equations, mechanics, and the interplay between these fields. Much of my recent effort has been directed toward the development of the finite element exterior calculus. In 2009 and 2010 I served as president of SIAM, the largest applied mathematics and computational science professional organization in the world. From 2001 to 2008 I directed the IMA, the world's leading interdisciplinary mathematical research institute.

Henrici Prize

I was awarded the Peter Henrici prize at the International Congress of Industrial and Applied Mathematics in Tokyo on August 20, 2023, cited for “fundamental contributions of extraordinary originality, depth, and impact to the finite element analysis of partial differential equations, ranking amongst the classics in numerical analysis literature”.

Doug Arnold and Ivo Babuska

In a SIAM News article entitled Remembering Ivo Babuška, I recall the extraordinary life and achievements of Ivo Babuška, who passed away in 2023 at the age of 97. Ivo was the preeminent authority on the finite element method and one of the creators of the field of computational science and engineering. There is also a PDF version of the article.

WAVE logo

I am a principal investigator of the Simons Collaboration on the Localization of Waves, an international group of leading mathematicians and physicists working together on some of the most compelling puzzles in modern condensed matter physics, with the support of the Simons Foundation.

My publication profile on Google scholarGoogle scholarMathSciNetMathSciNetORCID iDarXivORCID iDORCID
Selected research publications (complete list available here)
       The landscape law for tight-binding Hamiltonians   2022
       Spectral functions and localization-landscape theory in speckle potentials   2022
       Local L2-bounded commuting projections in FEEC   2021
       Complexes from complexes   2021
       Sharp estimates for the integrated density of states in Anderson tight-binding models   2021
       The Hellan-Herrmann-Johnson method with curved elements   2020
       Localization of eigenfunctions via an effective potential   2019
       Computing spectra without solving eigenvalue problems   2019
       Finite Element Exterior Calculus   2018
       Effective confining potential of quantum states in disordered media   2016
       Periodic table of the finite elements   2014
       Finite element exterior calculus: from Hodge theory to numerical stability   2010
Finite element exterior calculus, homological techniques and applications   2006
     “Any young (or not so young) mathematician who spends the time to master this paper
      will have tools that will be useful for his or her entire career.”
— Math Reviews
Differential complexes and numerical stability   2002
Unified analysis of discontinuous Galerkin methods for elliptic problems   2002
Mixed finite elements for elasticity   2002
Multigrid in H(div) and H(curl)   2000
A uniformly accurate finite element method for the Reissner-Mindlin plate   1989
A stable finite element for the Stokes equations   1984
An interior penalty finite element method with discontinuous elements   1982

Updated August 11, 2023