MATH 8445
Numerical Analysis of Differential Equations

Please fill in the final exam time survey.

Fall 2009, MWF 10:10-11:00 Vincent Hall 20

Instructor: Douglas N. Arnold

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

Office hours: Monday 2:30-3:30, Friday 11:10-12:00, and by appointment

• Homework 1, due 9/23/09 (solution to first problem: pdf, latex)
• Homework 2, due 10/12/09

About the course: This is the first semester of a two-semester graduate level introduction to the numerical solution of partial differential equations. The first semester will emphasize elliptic partial differential equations. It will begin with a relatively brief study of finite difference methods for the Laplacian and the basic techniques to analyze them. 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. The largest portion of the first semester will be devoted to finite element methods for elliptic problems, and their analysis. In the second semester we will study of the numerical analysis of time-dependent (parabolic and hyperbolic) partial differential equations, and more advanced topics in finite elements for elliptic problems. Lecture schedule Lecture notes Part 1: Finite differences; Linear algebraic solvers Part 2: Finite elements (in progress) Program code FEniCS tutorial
		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.

References: I will present the material in my own way, and students are expected to take notes. Much of the same material is covered in the following texts.

• Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, Randall J. Leveque, Society for Industrial and Applied Mathematics, 2007. (on reserve in Math Library)
• Finite elements: theory, fast solvers, and applications in solid mechanics, Dietrich Braess, third edition, Cambridge University Press, 2007. (available online through the library, 2nd edition on reserve in Math Library)
• Numerical solution of partial differential equations by the finite element method, Claes Johnson, Cambridge University Press, 1987. (on reserve in Math Library)
• The mathematical theory of finite element methods, Susanne Brenner and Ridgway Scott, third edition, Springer, 2008. (available online through the library and on reserve in Math Library)

Exams and homework: There will homework sets and/or computational projects every few weeks, a midterm, and a final exam.

Updated October 21, 2009