Foundations of the Finite Element Method

Math 635 (Fall 2008)

Instructor: Manil Suri

Basic Information

Manil Suri, Math/Psych 419, (410) 455-2311, suri@math.umbc.edu,
office hours: MW 4:00-5:00 or by appointment
Lectures: MW 5:30-6:45
Text: Finite Elements by Dietrich Braess (3rd edition)
Prerequisites: The textbook is such that a fair level of mathematical maturity will be required to follow it. This means that a good background in mathematical analysis (including being comfortable with proving theorems) as well as numerical analysis will be required. For those who have not taken Math 600 and Math 620 (or their equivalents), please talk to the instructor. Engineering students should have taken a theorem-proving course like Math 301 at a minimum. Programming will be done in Matlab.

Overview

Finite element methods are used to approximate the solutions of partial differential equations which arise in various engineering and other applications. This course will concentrate on the mathematical foundations of the method. The first several lectures will be devoted to developing the functional analysis required to analyze these methods. This will be followed by the description, error analysis and some illustrative computations with traditional `h' type methods (Chapter II of the text). Following this will be a similar treatment of `p' and `hp' type methods (not included in the text). The course will conclude with topics selected from other chapters of the text, such as mixed methods, a posteriori error estimators, parabolic problems, hyperbolic problems, applications to elasticity. (For parabolic and hyperbolic problems, some material from a book by Claes Johnson will be handed out.) There will be one project, which will be to write a finite element code in one dimension, and use it to investigate some of the theory developed.

Homework, Grading and Tests

There will be several homeworks assigned, and one project. There will be one in-class mid-term test. The final grade will take into account both homework and tests. The grade will be based on: HW: 55%, Project: 25% Test: 20%. Tentative date of the test is Oct 20th.

Academic Conduct

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, or the UMBC Policies section of the UMBC Directory.