MAP 6376: Finite element methods

Spring 2010. Section 7770.




Instructor
Jay Gopalakrishnan
Venue
Anderson Hall, AND 032 (revised!)
Times
Tuesdays 7:25-10:25am (periods 1-3)
Office hours
Tuesdays 3:00-4:00pm (in LIT 442) or by appointment (email me: jayg at ufl dot edu).

Prerequisites
  • Consent of the instructor.
  • MAP6375 is not a prerequisite.

Textbook
You are not required to purchase any textbook. Some advanced material will come from recent research papers. The following books can be useful reference material:

  • Theory and practice of finite elements, by Alexandre Ern and Jean-Luc Guermond.
  • The mathematical theory of finite element methods, by Susanne C. Brenner and L. Ridgway Scott.
  • The finite element method for elliptic problems, by Philippe G. Ciarlet. (Reprinted editions of this classic are available from SIAM.)

Online materials
Online course materials will be placed here (password protected).

Objective
This course introduces students to finite element methods for numerically solving some partial differential equations. Although topics are often introduced with engineering applications in mind, the course emphasizes mathematical rigor.

Outline
  • Approximation estimates in Sobolev spaces
  • Finite elements in an exact sequence
  • Interpolation theory and fractional estimates
  • A posteriori error estimators and adaptivity
  • Discontinuous Galerkin methods

Evaluation
Evaluation is based on class projects.

The Fine Print
  • University's honesty policy: All students are expected to know and abide by the University of Florida Honor Code.
  • Copyrighted materials: All course materials handed out in class or placed on the web are protected by copyright laws, and are for personal use only. Multiple copies or sale of these materials is prohibited.
  • Religious Holidays: In accordance with the university's policy, students upon prior notification of their instructors, shall be excused from class or other scheduled academic activity to observe a religious holy day of their faith.
  • Students with disabilities: Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to me when requesting accommodation.


Jay Gopalakrishnan