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Plenary address delivered at ICM 2002 International Congress of Mathematicians

Summary: Plenary address delivered at ICM 2002
International Congress of Mathematicians
Beijing, China, August 24, 2002
Differential complexes and
numerical stability
Douglas N. Arnold
January 20, 2003
Differential complexes such as the de Rham complex have recently come
to play an important role in the design and analysis of numerical methods for
partial differential equations. The design of stable discretizations of systems
of partial differential equations often hinges on capturing subtle aspects of
the structure of the system in the discretization. In many cases the differen-
tial geometric structure captured by a differential complex has proven to be a
key element, and a discrete differential complex which is appropriately related
to the original complex is essential. This new geometric viewpoint has pro-
vided a unifying understanding of a variety of innovative numerical methods
developed over recent decades and pointed the way to stable discretizations
of problems for which none were previously known, and it appears likely to
play an important role in attacking some currently intractable problems in


Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota


Collections: Mathematics