Numerical Analysis of Differential Equations 2nd semester

**Spring 2012,** MWF 10:10-11:00 Vincent Hall 313

**Instructor**: Douglas N. Arnold

**Contact info**: 512 Vincent Hall, telephone: 626-9137, email:

**Office hours**: Tuesday 3:35-4:25, Friday 2:30-3:20, and
by appointment

**Adjustments to class times**: There will be no class on
March 7, 9, or 26 or on April 4 or 13.

The last 10 lectures, starting April 11, will run 75 minutes, from 10:10 to 11:25.

- Lecture schedule
- Program code
- Lecture notes
- Homework 1, due 1/30/12

**About the course: ** This is the second semester of a two-semester graduate level
introduction to the numerical solution of partial differential equations. The
first semester course web page can be found here.
The primary prerequisite for this course is the material covered in the first
semester, especially the material on finite element methods, which can be
found in course notes for the
first semester.
In this semester we will study more advanced finite element methods, their properties,
and their analysis. We will begin with finite elements for the biharmonic equation, which
is used for modeling thin plates, among other things. The limitations of conforming
finite element methods will motivate us to study non-conforming methods
and mixed finite element methods, both of which we shall
also consider in the simpler case of second order problems. We will also consider
mixed methods for the Stokes viscous flow equations, which is another prototypical application of mixed methods,
and then the very important example of the elasticity equations,
including conforming, nonconforming, and mixed methods. Much of this material is generalized
and clarified by the recently developed *finite element exterior calculus*, which we
will glimpse later in the semester. Additional topics will be included as time allows.

Updated February 12, 2012