photo of D. Arnold

Douglas N. Arnold

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

I am a mathematician and 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. From January through July 2013, I am Leverhulme Visiting Professor at University of Cambridge.

Selected research publications (complete list available here)
New! • Tensor product finite element differential forms and their approximation properties   2012
• On the consistency of the combinatorial codifferential   2012
• Nonconforming tetrahedral mixed finite elements for elasticity   2012
       • Finite element exterior calculus for parabolic problems   2012
       • Spaces of finite element differential forms   2012
       • Finite element differential forms on cubical meshes   2012
       • Mathematicians take a stand (about the Elsevier boycott)  2012
       • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions   2011
       • The serendipity family of finite elements   2011
       • 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 December 29, 2012