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MATH 635 Foundations of the Finite Element Method

(Spring 2014)
Instructor: Manil Suri

Basic Information

  • Manil Suri, Math/Psych 419, x52311, suri@umbc.edu,
    office hours: MW 3:30-4:30 or by appointment
  • Lectures: MW 5:30-6:45
  • Text: Finite Elements by Dietrich Braess (3rd edition)
  • Prerequisites: A good background in mathematical and numerical analysis will be advantageous. Programming will be done in Matlab (or language of your choice).

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 theoretical foundations of the method. The first several lectures will be devoted to developing the mathematical analysis required to analyze these methods. This will be followed by the description, error analysis and some illustrative examples 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). Special attention will be paid to the approximation of singularities (such as those that develop at cracks). The course will conclude with selected topics of interest to the class, such as mixed methods, a posteriori error estimators, parabolic problems, hyperbolic problems, applications to elasticity, reliability.

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.

Learning Goals

This course has the following learning goals.

  • Knowledge of the mathematical theory of variational procedures and the finite element method. The idea is to have an understanding behind the “black box” of FEM codes. (Text readings and homework problems will assist in realizing this goal.)
  • Theoretical and practical understanding of convergence rates. (Text, homework and project work will assist in realizing this goal.)
  • Familiarity with some of the frontiers of finite element theory and applications. (These advanced topics will be chosen according to the interests of the class.)

Homework, Grading and Tests

There will be several homeworks assigned, and one project. Tentatively, there will be one in-class mid-term test (open book) and one take-home final. The final grade will tentatively be based on: HW: 45%, Project: 20% Test: 15% Final: 20%. The date for the test will be announced well in advance.Grading will be regular letter grades: A>85%, B>75%, C>60%, D>45%.

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.