22M:176
Finite Element Methods
Fall 1998
 

Contact/class information

Instructor:	Dr. David Stewart
Phone:	335-3832
Email:	dstewart@math.uiowa.edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office hours:	Tu,W 1:30-2:30
Class times:	MWF 9:30
Class location:	McLean Hall 118

You can see me outside the office hours provided it is mutually convenient.

Resources

• Assignments (as they are made ready)
• Assignment 1 (in HTML or in PDF).
• Programming assignment (HTML).
• MATLAB code for computing the triang1, next_tri from the triangle array: mk_nxt_tri.m.
• Luke Olson has come up with some MATLAB code for plotting the results for test problem no. 2.  His message and MATLAB code are here.
• Documents/notes etc.
• Distributions and function spaces (notes by D.E. Stewart)
• Notes on interpolation in one dimension (notes by D.E. Stewart)
• Programs/routines/algorithms
• FEMLAB-1D for solving one-dimensional two-point boundary value problems using adaptive finite elements under MATLAB. This is available as a zip'd library of m-files, along with a README file.
• Other resources:
• More will be put here as it comes available.

Description

22M:176 is about the Finite Element Method. This is perhaps the most important computational method for dealing with partial differential equations. We will first see this method in use for one-dimensional problems (that is, ordinary differential equations). But once that is mastered, we will show how this can be used for partial differential equations, such as Poisson's equation:

$$\frac{\partial^2u}{\partial x^2}+ \frac{\partial^2u}{\partial y^2} = f(x,y).$$

Textbook

Computational Differential Equations by K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Cambridge University Press (1996).

Syllabus

• Review (linear algebra, approximating functions, optimization)
• Galerkin method (abstract form)
• Two-point boundary value problems
• Elliptic partial differential equations (e.g. Poisson's equation)
• Error bounds and estimates
• Adaptive methods

If there is time, we might look at other PDE's (convection-diffusion, heat equation, wave equation).

Assessment

There will be two in-class exams (20% each), two assignments (15% each) which may include some programming, and a programming assignment (30%). There may also be ungraded homework assigned during the course.

Familiarity with MATLAB will be useful during the course.

Notes

The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes.

The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.

Please let you instructor know if you have a disability that requires special arrangements.
 

8/24/1998