Dept. of Mathematical Sciences | Fall 2004, UAF |

Tentative time & place:

**
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
different. I
propose to start the course using photocopies of the 1988
text.) |

To make the mathematics meaningful we should use Matlab to do as-simple-as-possible examples of finite element computations.

Prerequisites: Clearly 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. Such talks might be a:

(i) lecture on a topic not covered by Bueler's lectures

(ii) lecture on the content of a research paper, or

(iii) description and analysis of a nontrivial computation performed by the student.

Graduate students in mathematics, engineering, and geosciences are especially encouraged to attend.