Course Announcement

Spring 2002

Title: Numerical Solution of Partial Differential Equations

Course Number: MATH - 7610/7616

The numerical solution of partial differential equations using the finite difference and the finite element methods. Prerequisites MATH - 6640 or departmental approval.

The course is an introduction to the finite element and finite difference methods for solving boundary-value problems (partial differential equations) and initial-value, boundary-value problems (partial differential equations). We will introduce both the finite element and finite difference methods, contrast the two and see their similarities.

We will discuss stability, consistency, and convergence of finite difference schemes, and see error estimates and convergence results for the finite element method. The students will write numerical code to solve simple partial differential equations in order to get "hands on" experience with these methods.

Course outline.


  1. D. Braess; Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics}, Cambridge University Press, Cambridge, second ed., 2001.
  2. K. W. Morton and D. F. Mayers; Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, 1994.