# 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.

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:

26E15

Keywords: