MATH 5520: Finite Element Methods 1, Spring 2009

Tuesday and Thursday, 2:00am - 3:15am, MSB 118
Instructor: Dmitriy Leykekhman



Instructor: Dmitriy Leykekhman

Office Hour: 10:00-11:00 a.m. Tuesday and Thursday, at MSB 332

Prerequisites: Basic Linear Algebra. Some knowledge in MATLAB programming helps.

Textbook: "Numerical Solution of Partial Differential Equations by the Finite Element Method" by Claes Johnson.
Back to reprint by Dover Publications available at available at Amazon

Course workload: Homework will be assigned roughly once a week, mostly with MATLAB programming assignments and one final take-home project.

Credits: 3 credit hours.

Grading Policy : The final grade will be determined from the homework assignments and the final project.
You may organize study groups to discuss material and assignments, but you must write your own solutions.

Scope: This course is appropriate for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. I will try to make the course self contained. Familiarity with basic real analysis, partial differential equations, and functional analytical tools for Hilbert spaces is required. Basic knowledge of MATLAB is required. The material can be split into several part:
Topics covered:
Weak derivatives.
Sobolev spaces.
Imbedding theorems.
Weak solutions.
Existence and regularity.
Finite element spaces.
Approximation theory.
A priori error analysis.
Implementation issues.

Additional topics may include:
Time dependent problems.
Advection dominated problems.
A posteriori error estimates.
Applications.