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Douglas N. ArnoldMcKnight Presidential Professor of Mathematics 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 serve 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. |
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• Finite element exterior calculus: from Hodge theory to numerical stability 2009 |
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| • Stability of Lagrange elements for the mixed Laplacian 2009 | |
| • Geometric decompositions and local bases for spaces of finite element differential forms 2008 | |
| • 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 |
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| • 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 |