General	Homework	Programming	Demos	Links

MATH 6590, Fall 2009
Topics on Applied Mathematics: The Finite Element Method

Course description:
An introduction to the finite element method. We will cover the following contents: Sobolev spaces, weak(variational) formulation, Ritz-Galerkin method, existence and uniqueness of the solution, finite element spaces, error estimates, implementation.
Prerequisite: Math 4263 (Introduction to PDEs), Math 5043 and 5053 (Advanced Calculus), Math 5553 (Numerical Linear Algebra), or equivalents. Students should also be familiar with at least one of the following computer programming languages: Matlab, C/C++, Fortran.
(syllabus)
See Syllabus Attachment for university-wide rules regarding dropping a course, academic integrity, free tutoring, and office of student disability services.
Instructor: Yanqiu Wang
- Office: 441 MATH (405-744-5698)
- Office Hour: TTh 4-6pm or by appointment.
- Email: yqwang (AT) math.okstate.edu
Classroom and time:

Sec Classroom Time

351 MATH 428 MW 4:00-5:15pm
Textbook:
- The mathematical theory of finite element methods (3rd edition)
- Authors: Susanne C. Brenner and L. Ridgway Scott
- OSU students have online access to the entire book here. Or if you are off campus, use the off-campus library access.
Additional reading:
- C. Johnson, Numerical solution of partial differential equations by the finite element method, Cambridge University Press, 1987
- G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Wellesley-Cambridge Press, 1988
- P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1979 (or in Classics in Applied Mathematics, Vol 40, SIAM, Philadelphia, 2002)
- A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Springer, 2004
Grading Policy:
- 5 homework (100 pts)
- You sacrifice 5 points per day for each late homework assignments. Early submissions are always welcome.

Sec	Classroom	Time
351	MATH 428	MW 4:00-5:15pm

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Homework

Homework 1, due 09/09/2009. Solution to problem 2.
Homework 2, due 09/23/2009.
Homework 3, due 10/16/2009.
Homework 4, due 11/9/2009 (extended to 11/11/2009).
Homework 5, due 11/30/2009.

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Programming

Read about the Gaussian quadrature. Download and try the Matlab program lgwt.m from Matlab file exchange center (unzip the file first).
Read the matlab program for 1D linear FEM and try to run it for different problems. This files uses lgwt.m to do numerical integration.
This a PDF file describing a simple 2D triangular mesh data structure and also a list of several mesh generators.
This is a matlab demo program showing how to write a coarse mesh by hand and than refine it to get fine meshes. It uses the mesh data structure p, be, t defined in the PDF file above.

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Demos

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Links

The Mathworks (Matlab) There are many Matlab tutorials on the web. Here're a few of them to help you get started:
A Very Elementary MATLAB Tutorial, Matlab Summary and Tutorial, Matlab Tutorial, A nice collection of Matlab tutorials, Matlab programming in Wikibooks
Octave is a free substitution for Matlab. Try this in case you don't have access to Matlab.
Octave in Wikibooks

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MATH 6590, Fall 2009 Topics on Applied Mathematics: The Finite Element Method

Course description:

Instructor: Yanqiu Wang

Classroom and time:

Textbook:

Additional reading:

Grading Policy:

Homework

Programming

Demos

Links

MATH 6590, Fall 2009
Topics on Applied Mathematics: The Finite Element Method