Fall 2012, MWF 10:1011:00 Vincent Hall 207 
Instructor: Douglas N. Arnold 
Contact info: 512 Vincent Hall, tel: 69137, email:

Office hours: Monday 3:304:20, Wednesday 2:303:20, and by appointment 
About the course: This is the first semester of a twosemester graduate level
introduction to the numerical solution of partial differential equations.
In the first semester
will begin with finite difference methods for the Laplacian
and the basic techniques to analyze them (maximum principle, Fourier analysis,
energy estimates). It will then continue with a study of
numerical linear algebra relevant to solution of discretized PDEs, such as those arising
from the finite difference discretization of the Laplacian (classical iterations,
conjugate gradients, multigrid). The largest portion of the
first semester will be devoted to finite element methods for elliptic problems,
and their analysis. The semester will conclude with the use of finite difference
and finite element methods to solve timedependent problems. The course will include
computational examples and projects using
Matlab, and, especially, the FEniCS software suite. A feature of the course is that
we will emphasize a uniform framework based on consistency and stability to analyze
both finite element and finite difference methods, for both stationary and
timedependent problems.




The cost for inadequate numerical analysis can be high. The first time
this offshore platform was installed, it
crashed to the sea bottom causing a seismic event measuring 3.0 on the
Richter scale and costing $700,000,000. The cause: flawed algorithms for
the numerical solution of the relevant partial differential equations.
For more information see here.

