### Math 3072: Finite Element Method

**Instructor:** Catalin Trenchea

Phone: (412) 624-5681

E-mail: trenchea@pitt.edu

Office: Thackeray 606

**Lecture:** MWF 10:00-10:50 THACKERAY 524

**Office Hours:**
Tu 10:00am-noon, Thu 10:00am-noon and by appointment

**Textbook:**
The course will not follow closely a specific text book. The book *Understanding
and Implementing the Finite Element Method*, by Mark Gockenbach, SIAM
2006, will be used as a reference on implementation issues.

**Prerequisites:**
Good undergraduate background in linear algebra and advanced
calculus. Familiarity with partial differential equations will be useful.

**Content:**
This course is an introduction to the theoretical and computational aspects
of the finite element method for the solution of boundary value problems for partial
differential equations. Emphasis will be on linear elliptic, self-adjoint, second-order
problems, and some material will cover time dependent problems as well as nonlinear
problems. Topics include: Sobolev spaces, variational formulation of boundary value
problems, natural and essential boundary conditions, Lax-Milgram lemma, approximation
theory, error estimates, element construction, continuous, discontinuous, and
mixed finite element methods, and solution methods for the resulting finite element
systems.

**Topics to be covered:**
FEM for two point boundary value problems, Brief introduction to Sobolev Spaces, FEM for elliptic equations, Approximation theory for FEM, Non-conforming and mixed FEM, FEM for parabolic equations, FEM for advection diffusion equations, FEM for hyperbolic equations.

**Homework:**
Written homework and several computational projects will be assigned.
Suggested programming languages are FreeFEM and Matlab. In the computational projects we will
utilize the software provided with the textbook.

**Exams:**
There will be one in-class midterm exam, a paper presentation, and a final
project.

#### Other references:

*The mathematical theory of finite element methods*, S. C. Brenner and L. R.
Scott, Springer-Verlag 1994.

*Finite elements, 2nd ed.*, D. Braess, Cambridge 2001.

*The Finite Element Method for Elliptic Problems*, Philippe G. Ciarlet, SIAM 2002.

*Numerical Solutions of Partial Differential Equations by FEM*, Claes Johnson,
Studentlitteratur 1987.

*Finite element solution of boundary value problems*, O. Axelsson and V. A.
Barker, SIAM 2001.

The course web page will be updated continuously throughout the semester.
The student is responsible for checking this web page for assignements
and policies.

If you have a disability for which you are or may be requesting an
accodomation, you are encouraged to contact both your instructor
and the Office of Disability Resources and Services, 216 William Pitt
Union, (412) 648-7890/(412) 383-7355 (TTY), as early as possible in the term. DRS will verify
your disability and determine reasonable accomodations for this course.