Class Meeting Time:
Tuesday, Thursday 2:00pm - 3:15pm, MCB 204

Office Hours:
Tuesday, Thursday 4:00pm - 5:00pm

Course Objectives:
Math 5484 is a general introduction to the finite element method. It will focus on both mathematical and computational topics. Since this course serves as a basis for a preliminary exam in the department of mathematics, a special emphasis will be posed on proofs.

The objectives are:
  (1) to introduce the basic mathematical tools used in the development and analysis of the finite element method; and
  (2) to introduce the basic computational methods for the numerical discretization of the finite element algorithms.

At the end of the course, every student should be able to:
  (i) discretize a simple partial differential equation by using the finite element method; and
  (ii) analyze the resulting finite element discretization.

We will start by illustrating the finite element method for a simple partial differential equation, pointing out the main mathematical and computational steps. We will continue by investigating in detail each step, covering both theoretical and practical aspects, such as weak formulations of boundary-value problems, finite element spaces, approximation theory for finite element spaces, error estimates, mixed methods, effects of numerical integration and curved boundaries, nonconforming methods, time-dependent problems, data structuring, mesh generation, numerical quadrature, assembling, storage, and linear algebra.

Text:
Numerical Solution of Partial Differential Equations by the Finite Element Method, by C. Johnson, Dover Publications, 1st edition (2009), ISBN: 048646900X.

Prerequisites:
Basic background in partial differential equations and their approximation by numerical methods. Students should be able to use a programming language (such as MATLAB, FORTRAN, or C) to complete their computational assignments.

Evaluation Criteria and Grading:
There will be a midterm exam, a final exam, and a final project. The midterm exam will count 20%, the final exam will count 30%, and the project will count 30%. There will be homework assignments, which will count 20%. A score of 90% will guarantee an A-, 80% a B-, 70% a C-, and 60% a D-.

Missed Work:
If a student fails to take an exam or quiz, his/her score is zero unless the reasons for the failure are serious and beyond the student's control (``subc''). The instructor reserves the right to verify that the reasons are serious and beyond the student control. It is to the student's advantage to inform the instructor of such reasons before missing the work. When work is missed for ``subc'' reasons, the instructor, after consultation with the student, will decide how to handle the missed work.

Honor:
Students work on in-class exams alone. There will be NO books, notes, calculators, etc. allowed on the exam. The honor code applies to all graded work in this course. The Undergraduate Honor Code pledge that each member of the university community agrees to abide by states: “As a Hokie, I will conduct myself with honor and integrity at all times. I will not lie, cheat, or steal, nor will I accept the actions of those who do.” Students enrolled in this course are responsible for abiding by the Honor Code. A student who has doubts about how the Honor Code applies to any assignment is responsible for obtaining specific guidance from the course instructor before submitting the assignment for evaluation. Ignorance of the rules does not exclude any member of the University community from the requirements and expectations of the Honor Code. For additional information about the Honor Code, please visit: https://www.honorsystem.vt.edu/

Special Needs:
If you need adaptations or special accommodations because of a disability (learning disability, attention deficit disorder, psychological, physical, etc.), if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible.

IMPORTANT:
If you are not on the class roll that comes out after the last add date, immediately check your schedule at a terminal and start attending the proper section. For no foreseeable reason (computer and registrar personnel mistakes included) will you be allowed to stay in the wrong section or to drop a section for which you are actually enrolled after the last drop date. By simply attending a section you will not be placed on its roll.