MATH 8445
Numerical Analysis of Differential Equations 1st semester

Fall 2012, MWF 10:10-11:00 Vincent Hall 207
Instructor: Douglas N. Arnold
Contact info: 512 Vincent Hall, tel: 6-9137, email: 
Office hours: Monday 3:30-4:20, Wednesday 2:30-3:20, and by appointment

About the course: This is the first semester of a two-semester 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 time-dependent 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 time-dependent problems.

Sleipner

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.

Text and syllabus: The course will follows these Lecture Notes. The table of contents may be taken as the syllabus for the course.

Other references: Similar material is covered in the following texts. These are all on reserve in the Math Library and several have electronic editions available through the library.

Exams and homework: There will be homework sets and computational projects, a midterm (on October 26, classtime), and a final exam (December 18, 8:00AM-10:00AM).

Additional material:


Updated December 12, 2012