MATH 679-002
Fall 2012

Analysis of the Finite Element Method


| About the Course | Instructor | Prerequisites | Learning Outcomes | Course Evaluation | Course Outline | Lectures/HW/Project | MATLAB | Academic Integrity | Disability Accomodation |

ABOUT THE COURSE

Partial differential equations arise in the mathematical modeling of many physical, chemical and biological phenomena and many diverse subject areas such as fl uid dynamics, electromagnetism, material science, astrophysics, economy, financial modelling, etc. Often the equations under consideration are so complicated that finding their analytical solutions in closed form is either impossible or impractical, and one has to resort to seeking numerical approximations to the unknown analytical solution. This course is devoted to a special class of numerical techniques for the approximate solution of partial differential equations: finite element methods (FEM). The objective of this course is to provide a mathematical background that explains the working of finite elements, their construction, capabilities and limitations, stability and convergence. An introduction to various new advances in the field will also be provided along with an opportunity for the students to implement the method in practice. The viewpoint will be modern, with connections made between each topic and a variety of applications. By the end of the course, the student should not only be familiar, but more confident, in effectively using finite element methods to solve problems in their own field of interest.

INSTRUCTOR

Dr. Padmanabhan Seshaiyer

PREREQUISITES

Sufficient recall of Calculus, Linear Algebra, Differential Equations and computer literacy including familiarity with MATLAB. A course in Numerical Analysis or knowledge of numerical integration, solution to linear systems of equations, interpolation and approximation is recommended.

EXPECTED LEARNING OUTCOMES

In this course, the emphasis will be to expose the students to the mathematical and computational aspects of the finite element methods. The objective will be to train students to understand why the methods work, how to evaluate stabilty and convergence of these methods along with what type of errors to expect when this method is implemented in practice. The expected learning outcomes for the course will be assessed through: Exams, homeworks, projects, in-class activities and class discussions. Problem-based learning will be an integral part of the course.

COURSE EVALUATION

Evaluation for the course will be based on the following criteria:

Homework 50%
Course Project 25%
Final Exam 25%
TOTAL 100%

There will be five homework assignments during the semester each worth 10 %. There will also be a course project which is worth 25 % and will involve using the finite element method (with some programming) to solve a problem of your choice, reading, reporting on a paper concerning aspects of the finite element method beyond those covered in class. There will be one comprehensive final exam in this course. Make-up exams may be possible only in the case of documented emergencies. The Final Exam will be on Thursday, Dec 13, 2012 from 7:30 PM - 10:15 PM and will be comprehensive. Make-up exams may be possible only in the case of documented emergencies.

COURSE OUTLINE

We plan to cover the following topics in this class. Please note that topics covered may vary slightly from those below depending on class interest and time. The primary reference will be lecture notes provided by the instructor that will be posted on the course website on a regular basis.

LECTURES/HOMEWORK/PROJECT

MATLAB

MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions. MATLAB will be used for scientific computation, analysis and presentation of data in the course.

ACADEMIC INTEGRITY

All students will be expected to abide by the Honor Code: Student members of the George Mason University community pledge not to cheat, plagiarize, steal, or lie in matters related to academic work .

DISABILITY ACCOMODATION

Any student who, because of a disability, may require some special arrangements in order to meet course requirements should contact the instructor as soon as possible to make such accommodations as may be necessary.