MTH 652: Advanced Numerical Analysis
Winter 2012
Instructor
Jay Gopalakrishnan
Venue
Clay 104
Times
Tue, Thu: 12:00-13:15
Office hours
Tue 13:15-14:15 (in NH 309)
or by appointment (email: gjay@pdx.edu).
Objective
Partial differential equations model many natural and
technological processes. This course aims to teach
computational techniques for rapidly solving such equations.
Outline
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.
References
- Partial differential equations with numerical methods,
by Stig Larsson and Vidar Thomée.
Springer-Verlag, Berlin, 2003.
- Theory and practice of finite elements,
by Alexandre Ern and Jean-Luc Guermond.
Springer-Verlag, 2003.
- 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.
Evaluation
Grades will be assigned based on take-home exams.
Jay Gopalakrishnan