Introduction to finite element exterior calculus

Saturday, October 30, 2010 - 3:30pm - 5:00pm
Keller 3-180
Ragnar Winther (University of Oslo)
The purpose of this tutorial is to give an introduction to
finite element exterior calculus, targeted to an audience which is
reasonably familiar with topics like elliptic
partial differential equations, Sobolev spaces, and finite element
methods. We will first give a brief review of some of the fundamental
concepts of exterior calculus, such as interior and exterior products,
pullbacks, the Hodge star operation, the exterior derivative, and
Stokes' theorem. Then we will focus on some of the main building blocks
of finite element exterior calculus. In particular, we will discuss
piecewise polynomial spaces of differential forms, degress of freedom,
and the construction of bounded cochain projections. In addition,
an abstract theory of Hilbert complexes will be presented, and we will
explain how this relates to
to the stability theory for approximations of the Hodge Laplacian.
MSC Code: