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

The schedule for the course can be found via the link to webTimeEdit top of the page.

Course code GU: MMA430

Teachers

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.

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.

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