Instructor: Prof. Yves Bourgault
Email: ybourg@uottawa.ca

Course Dates: January 10th - April 7th, 2024
Mid-Semester Break: February 19th - 23rd, 2024
Lecture Times: Wednesdays 1:00 PM - 2:20 PM | Fridays 11:30 AM - 12:50 PM (ET) - Last lecture is on Tuesday, April 7th, 2024, 11:30 AM - 12:50 PM (EDT)!
Office Hours: Mondays 1:00 PM - 2:00 PM & Wednesdays 3:00 PM - 4:00 PM (ET) | Location - University of Ottawa, STEM Building, Room 517 & via Zoom

Registration Fee: PSU Students - Free | Other Students - CAD$500

Capacity Limit: 35 students

Format: Hybrid synchronous delivery

• In-Person - University of Ottawa, Morisset Hall, Room 250
• Online - via Zoom

Course Description

Brief review of partial differential equations (PDEs), particular problems for elliptic, parabolic and hyperbolic PDEs. Presentation of finite difference and finite element methods, numerical solution of the discrete problems. Numerical analysis of the two methods: stability, consistency and convergence, spectral analysis of finite difference methods, error estimates. More advanced topics will be covered, such as time-stepping methods for parabolic equations, stabilization techniques, error estimates and mesh adaptation, etc. The course includes implementation of the methods and numerical experiments using free software.

Prerequisites: (recommended) Multivariate Calculus, Real Analysis, Differential Equation, knowledge of a programming language

Evaluation:
The tentative rubric for this course is:

• Mini-Projects - 60%
• Final Exam – 40%

Mini-Projects: The five mini-projects will include theoretical questions, implementation and practical applications of the numerical methods using Octave and FreeFem++ (both freeware). Mini-projects can be done individually or in team of two students.

Final Exam: The final exam will be on theoretical aspects of the course. It will last three hours and be written in-person for uOttawa & Carleton students at a time during the final exam period (April 12th-25th). The students from other institutions will write a 24-hour take-home exam during this same final exam period.

Resources:
The following textbooks and software will be used in the course:

• A. Quarteroni, Numerical Models for Differential Problems, Springer, 2014 https://link.springer.com/book/10.1007/978-88-470-5522-3
• S. Bartels, Numerical Approximation of Partial Differential Equations, Springer, 2016 https://link.springer.com/book/10.1007/978-3-319-32354-1
• Octave, or Matlab if you prefer https://octave.org/
• FreeFem++ https://freefem.org/