  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 differential
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 provided 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 numerical
PDE.
