Research interests of Douglas N. Arnold
My primary research interests are in numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields. Much of my work concerns the computer solution of partial differential equations, focusing on the development and understanding of methods for simulating physical phenomena ranging from the deformation of elastic plates and shells to the collision of black holes. Since 2002 a lot of my effort has been devoted to the development of the finite element exterior calculus, a new approach to the stability of finite element methods based on geometric and topological structure underlying the relevant partial differential equations. I gratefully acknowledge the long term support of my research by the National Science Foundation.
Updated February 14, 2009