Course Description
This course presents the basic mathematical theory of the
finite element method for incompressible flows. It also covers related
computational algorithms and computer implementation details.
It is intended primarily for graduate students interested either
in developing modern and rigorous skills in the numerical solution
of fluid mechanics problems, or in developing further their basic skills
in the finite element methodology. Using the Poisson equation as a background problem,
the course begins with a fast review of the basic finite element method for simple elliptic problems.
Next, it explains why this basic theory is insufficient for problems
such as the mixed formulation of elliptic equations, incompressible flows,
the advectiondiffusion problem, and the NavierStokes equations.
To address such problems, the course continues with
notions of the mathematical analysis of non coercive
partial differential equations, the infsup (or BabuskaBrezzi) condition and its application
to the Stokes and Darcy problems, and a presentation of stable mixed finite element methods
and corresponding algebraic solvers. Stabilization approaches are then discussed in the
context of the advectiondiffusion equation. Finally, the numerical solution of the
incompressible NavierStokes equations by a suitable finite element method is covered.
The course material described above is complemented by a balanced set of theoretical, computational,
and Matlab computer programming homeworks.
Contact Information
Instructor:  

Course
Assistants: 



Lectures
Time:  Tuesdays and Thursdays 1:15 to 3:05 PM 
Location:  Rm 240110 
Prerequisites
Textbook
There is no required textbook for this class.
Homework
There will be assignments due roughly every two weeks. Collaboration among students is encouraged. You should feel free to discuss problems with your fellow students (please document on each assignment with whom you worked). However, you must write your own solutions, and copying homework from another student (past or present) is forbidden. The Stanford Honor Code will apply to all assignments, both in and out of class.
Exams
There will be no midterm. There will be a final exam. It is open notes and open book.
Grading
The course grade will be based on assignments (50%) and the final exam (50%).