Hilbert complexes and the finite element exterior calculus

Monday, November 1, 2010 - 10:00am - 10:45am
Keller 3-180
Douglas Arnold (University of Minnesota, Twin Cities)
The finite element exterior calculus, FEEC, has provided a
viewpoint from which to understand and develop stable finite
element methods for a variety of problems. It has enabled us to
unify, clarify, and refine many of the classical mixed finite
element methods, and has enabled the development of previously
elusive stable mixed finite elements for elasticity. Just as
an abstract Hilbert space framework helps clarify the theory of
finite elements for model elliptic problems, abstract Hilbert
complexes provides a natural framework for FEEC. In this talk
we will survey the basic theory of Hilbert complexes and their
discretization, discuss their applications to finite element
methods. In particular, we will emphasize the role of two key
properties, the subcomplex property and the bounded cochain
projection property, in insuring stability of discretizations
by transferring to the discrete level the structures that insure
well-posedness of the PDE problem at the continuous level.
MSC Code: