Important announcements will be put here during the semester. It is a good idea to check this space regularly before the class of before you want to come to my office.

The objectives of the class are

• to learn the basic principles of finite element methods
• to learn how the methods work and why sometimes they do not work
• to gain understanding of common data structures in Finite Element software
  
• to establish  good habits in the development and testing of  scientific software
• have a through undertainding of the material and be able to use it
  

Material to be covered (tentative):

1. Finite element methods for elliptic problems (Ch. 0, 1 of Johnson, Ch. 1 of Hughes)
2. Abstract formulation and error estimates (Ch. 2 of Johnson, Ch. 2 of Hughes)
3. Isoparametric elements and programming techniques (Ch. 3, 11 of Hughes)
4. Approximation of functions by finite elements (Ch. 3,4 of Johnson)
5. Linearized elasticity (Ch. 5.1 of Johnson, Ch. 2 and selected sections of Ch. 4, 5 of Hughes)
6. Mixed and nonconforming methods (Ch. 5.2, 11 of Johnson,  additional reading)
   
7. Time-dependent problems and vibration (Ch. 8 of Johnson, selected sections of Ch. 7 of Hughes)
8. We will develop together a Finite Element software in Matlab to illustrate the concepts and run experiments.
   

Assignments and tests

There will be about 5-6 homeworks given on Mondays and due always the following Monday, mostly consisting of exercises from the textbooks. Homeworks will be considered on time if they are turned in on the due date at the beginning of the class or left at my office before the class. LATE HOMEWORKS WILL NOT BE GRADED. Each student will get over the semester several software tasks consisting of the development or validation of small parts of the  Matlab software. Each task will be due in a week and will be completed by an in-class live demonstration. Because the progress of the class will depend on the timely completion of the tasks, I WILL HAVE TO COMPLETE LATE OR INCORRECT TASKS MYSELF AND THE STUDENT WILL RECEIVE NO OR REDUCED CREDIT. Each student will complete a computer project consisting of experiments or a more extensive addition to the Matlab software over last 4-6 weeks concluded by a 15 minute presentation. There will be a midterm and final exams in class. You cannot use any books, computers, or notes at the exams, except for one 3" by 5" card where you can write anything you want. The midterm will be on October 20. The final will be during the finals week as determined by the Auraria finals schedule.

The progress of the class will be recorded and all assigments available in the class notes file. In-class computer demonstrations (there will be many of them) and the Finite Element software that we develop will be in the Matlab directory. Photos of whiteboards will be in the photos directory and from time to time assembled into a single photos file, which is much smaller. Handouts are in the handouts directory. You can access the files in the class web site more easily from your shell session on math as /home/faculty/jmandel/public_html/classes/5663f04

I enjoy discussing technical topics related to the class with my students during my office hours or any other time you walk in, but  please do your homeworks and tasks ahead of time, and try not to come to my office right before the homework or the task is due and expect me to do it for you.

Computer assignments must be turned in as file on our server, math.cudenver.edu. Assignments must be done in Matlab. Most Matlab assignments can be done by simply editing M-files without any graphics; for graphics or to use the Matlab GUI, please use the Graduate Lab on 6th floor of the UCD building.  For every assignment, prepare a directory  named 5663 in your home directory on math, then in the directory 5663 make directory hw1 for homework 1, task1 for task 1, etc., and project for the project. Your directory should contain a working code and any relevant data that  was used to produce your printout.  All code should be run from a single Matlab file named go.m. The program has to run on math and be in the specified directory to receive any credit. Please turn in a  printout with all files and the output exactly as it is on math. You can prepare the assignment using another computer, such as a PC running Matlab (these are available in the undergraduate lab, SI 130, or you may purchase a student version of Matlab available at the campus bookstore for your own PC), but you must copy the files to math in the correct place and test that they run correctly.

Grading

The score will be determined by the sum of the best 3 out out of the following 5, each scaled separately from 0 to 33 1/3 points: 1. homeworks 2. software tasks 3. computer project 4. midterm 5. final. The letter grades will be A >= 90,  A- >= 85, B+ >= 80, B >= 75, B- >=70,  C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40.

• log in by ssh to math.cudenver.edu (ssh is standard on Linux. On Windows, download and install a copy of SSH Windows Client from http://www-math.cudenver.edu/downloads, which is accessible from all UCD computers
• if you have any problem with the system, email trouble@math.cudenver.edu, but, for password problems, note that our account and password policy does not allow to send passwords by email or, in most cases, give passwords over the phone.
• handouts with basic Unix commands are available at CINS
• for more information on our systems, see the computing systems overview 
• to edit files, you can use vi (for Unix knowledgeable people only) or pico (text mode, over a phone connection).
• to start Matlab, type matlab This will start the GUI if you are on an X-windows workstation and if your ssh forwards the X11 graphics, and in command line mode (without GUI) otherwise.  In command mode, the best way to edit files is simply open  another window to run the editor.
• for Matlab documentation and tutorials, see my Matlab links
• to compile and run Fortran program file.f, type
    g77 file.f ; a.out
• for Fortran documentation, see my Fortran links

Useful links and further reading

• Matlab links
• Fortran links
• Netlib
• Introduction to the Finite Element Methods by Niels Saabye Ottosen, and Hans Petersson , Prentice-Hall, 1992
  
• Finite element courses by Carlos Felippa at CU -Boulder (online fulltext)
• Fundamentals of Finite Element Analysis by David V. Hutton
  
• The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet, Elsevier 1978; reprinted SIAM 2002 
• The Mathematical Theory of Finite Element Methods by Susanne C. Brenner and L. Ridgway Scott, 2nd ed., Springer 2002
• Mixed and Hybrid Finite Element Methods by M. Fortin and F. Brezzi, Springer 1991
  
• Distmesh - A simple mesh generator in Matlab by Per-Olof Persson
  

Last updated 10/18/04