MTH 652: Advanced Numerical Analysis

Winter 2012

Jay Gopalakrishnan
Clay 104
Tue, Thu: 12:00-13:15
Office hours
Tue 13:15-14:15 (in NH 309) or by appointment (email:

Partial differential equations model many natural and technological processes. This course aims to teach computational techniques for rapidly solving such equations.

This is the second part of a three-part year-long advanced sequence on techniques for scientific computation.
Plan for this quarter (Part 2) :

  • Finite difference methods
  • Simple elliptic, parabolic, and hyperbolic equations. Discrete and exact maximum principles. Error analyses in energy and max-norms.
  • Finite element methods
  • Basic idea of Galerkin methods. Energy analyses. Approximation in Sobolev spaces. Exact sequences. Mixed methods.

  1. Partial differential equations with numerical methods, by Stig Larsson and Vidar Thomée. Springer-Verlag, Berlin, 2003.
  2. Theory and practice of finite elements, by Alexandre Ern and Jean-Luc Guermond. Springer-Verlag, 2003.
  3. The mathematical theory of finite element methods, by Susanne Brenner and L. Ridgway Scott, Second edition, 2002.

Students are not required to buy any of these.

Grades will be assigned based on take-home exams.

Jay Gopalakrishnan