MATH610: Numerical Methods for PDE's, Spring 2008

General information

• Instructor: Dr. Raytcho Lazarov, Blocker 505C, 845 7578
• Teaching Assistants: Dimitar Trenev, Blocker 605E, 845-7652
• Time: TR 11:10 -- 12:25 pm (regular class), W 4:10 pm -- 5:00 pm computer lab
• Classroom: CE 136 (regular class), BLOC 126 computer lab
• Office Hours: TR 10:00 pm -- 11:00 am or by appointment
• Texts: PDEs with numerical methods, by S. Larson and V. Thomee, Springer, 2003, and Numerical Methods for Elliptic and Parabolic PDEs, by P. Knabner and L. Angerman, Springer, 2003, (additional) Theory and practice of finite elements, by A. Ern and J-L Guermond, Springer, 2004.

Course description

• This is a one-semester course on numerical methods for partial differential equations. The course will focus on the basic concepts of the finite element method for elliptic boundary value problems. These will include a weak (variational) formulation of the problem and relies on the coercivity and continuity of certain bilinear forms in the simplest setting (and inf-sup condition in more general cases), approximation theory by piece-wise polynomial functions over partition of the domain into finite elements, error analysis, stability, and variational "crimes". Further, some basic techniques of finite differences and finite volumes will be introduced and discussed. Maximum principle, energy type estimates, and Fourier mode analysis will be used for studying the stability and accuracy of these methods applied to for elliptic, parabolic and hyperbolic problems.
  Graphics, grid generation, program implementation and simple iterative techniques will be discussed (mostly in the labs) in order to help you with the programming assignments. Programming skills (e.g. C, C++ or Matlab) are essential.
• This course, with MATH 609, form an one-year course on numerical analysis at graduate level. The sequence MATH 609 and MATH 610 serves as a basis for the qualifier on Numerical Analysis .

Exam Schedule

• Test #1, Thursday, February 14, 2008,
• Test #2, Thursday, March 27, 2008,
• Final exam, Friday, May 2, 2008, in class, 3:00 -- 5:00 pm.

Grading Policy

• Your grade for the course will be computed as follows:
  • (a) 15% will be determined by the programming assignments .
  • (b) 60% will be determined by the three exams (the final is comprehensive and enters with a double weight).
  • (c) 25% will be determined by the homework assignments .
• your MINIMUM grade will be A, B, C, or D, for averages of 90%, 75%, 60%, or 50%, respectively.