Latest news
2013-04-02: Updated the program and hand-in problems for week 2.
Welcome to the course.
The schedule for the course can be found via the link to webTimeEdit top of the page.
Course code GU: MMA430
Teachers
Lecturer: Stig Larsson
Assistant: Matteo Molteni
Course literature
S. Larsson and V. Thomée, Partial Differential Equations with Numerical Methods,
Texts in Applied Mathematics 45, Springer, 2003. Corrected second printing 2005.
Now in softcover, 2009.
Programme
Syllabus

Lectures and exercises

Week Chapter
Contents
  1 Tuesday   1, 3.1   Elliptic problems
  1 Wednesday   Appendix A   Sobolev spaces
  1 Friday   Appendix A   Calculus inequalities.




  Easter break



  2 Tuesday   3.4   Fundamental solution. Green's function.
  2 Wednesday     Exercises A.9, A.10, A.11, A.13(b), A.15.
  2 Friday   3.5   Riesz repr. thm, Lax-Milgram. Variational formulation of elliptic problems.



  3 Tuesday   3.6, 3.7, 5.2   Neumann's problem. Regularity. FEM in 2-D.
  3 Wednesday   Exercises 3.5, 3.9, 3.11, 3.13
  3 Friday   5.3, 5.4, 5.5   Error analysis for FEM.

 
  4 Tuesday   5.5, 5.6   FEM.
  4 Wednesday     Exercises 5.6, 5.8, 5.12
  4 Friday   8.1, 8.2   Parabolic problems.
     
  5 Tuesday   8.2, 8.3   Parabolic problems.
  5 Wednesday   ---   No lecture. May 1.
  5 Friday   8.4   The maximum principle.
     
  6 Tuesday   10.1-2   FEM for parabolic problems.
  6 Wednesday   10.2   FEM for parabolic problems. Exercises 10.3, 10.4.
  6 Friday     No lecture.
     
  7 Tuesday   10.2, 11.2   Time discretization of the heat equation. The wave equation.
  7 Wednesday     FEniCS tutorial (Matteo Molteni)
  7 Friday   11.3   First order hyperbolic equations.
     
  8 Tuesday   11.4   Hyperbolic systems.
  8 Wednesday   12   Finite difference methods for hyperbolic problems
  8 Friday     No lecture. Matteo Molteni available for consultation in his office 10-12.
     
Computer labs
Computer exercise (2 bonus points). Hand in before the exam. We use the FEniCS software. Install it on your computer!
Course requirements
Important theorems:
A.4, A.6, 3.1, 3.2, 3.6, 3.8, 5.3, 5.4, 5.5, 5.6, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 10.1, 10.2, 10.5, 11.1, 11.2, 11.3, 11.4, 11.5, 12.1
Assignments
Hand-in exercises
You should try to do all exercises for each chapter that we study. I invite you to hand in one set of exercise problems according to the list below. Each good set of solutions may give you 1 bonus point, maximally 6 points in the exam + 2 points for the computer exercise.
Week Excercises
  2   A.7, A.13(a), A.14, and A.16. Hand in on Friday week 2.
  3   3.4 and 3.6. Hand in on Tuesday week 4.
  4   5.1, 5.11, 5.19. Hand in on Tuesday week 5.
  5   8.5, 8.11. Hand in on Tuesday week 6.
  6   10.5 and 10.6. Hand in on Tuesday week 7.
  7  11.4, 11.7, 11.10. Hand in before the exam.
  8   Computer exercise (2 bonus points). Hand in before the exam.
Examination
Written exam.
Examination procedures
In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to take the examination. You do this at Chalmers Student Portal.

Notice of result is obtained only by email via Ladok. (Not verbally at study expedition.) This is done automatically when the results are registered. Check that you have the right grades and score.

At the annual examination:
When it is practical a separate review is arranged. The date of the review will be announced here on the course website. Anyone who can not participate in the review may thereafter retrieve and review their exam on Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and picked up at the Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.
Old exams
130830, 130528, 130114, 120831, 120522, 110826, 110524, 100525, 100827, 080526, 061024, 060828, 051019, 031022