|Dept. of Mathematical Sciences
||Fall 2004, UAF
Graduate Seminar in Finite Elements (Math 692)
Organizer/First Presenter: Ed
Tentative time & place: Wednesday,
I propose: A seminar in the basic mathematics of the finite element
method for partial differential equations. To control technical
difficulties I propose to limit the seminar to two spatial variables
and to primarily concern ourselves with linear elliptic and parabolic
problems, but with an eye toward nonlinear problems.
To give structure to the seminar I propose to give at least
the first six lectures from the small book:
Claes Johnson, Numerical
Solution of PDEs by the Finite
Element.Method, Cambridge University Press 1988.
(It is out of print. There is a 1996 version, quite
propose to start the course using photocopies of the 1988
The seminar will serve as a
introduction to Sobolev spaces
in the one and two variable cases and with many technical details
suppressed. The finite element method involves converting
PDE into a bilinear form on such spaces (i.e. a translation to the
"variational" form of the PDE). One then approximates
Sobolev space by a finite-dimensional subspace of
functions (the space of "finite
To make the mathematics meaningful we should use Matlab
to do as-simple-as-possible
examples of finite element computations.
one must have seen classical PDEs as taught in Math 421, and one must
be comfortable with linear algebra. Furthermore, either exposure
to real analysis (Math 641) or methods of mathematical physics (Math
611) is strongly recommended because function spaces will be the object
of interest from the beginning.
Students who want 2.0 credits
should be prepared to do up to six homework assignments during the
semester, using Matlab and certain FE tools, and give a one--hour talk.
talks might be a:
(i) lecture on a topic not covered by Bueler's
(ii) lecture on the content of a research paper, or
(iii) description and analysis of a nontrivial
performed by the student.
Graduate students in mathematics, engineering, and geosciences are
Ed Bueler at email@example.com or x7693 or Chapman
The first meeting on Wednesday, 8
September will include setting up a