# TMA4212 Numerical solution of differential equations by difference methods

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20.05 | The exam and a sketch of the solution. |

12.05 | Some rough sketch of how the theory problems of Exercise 5 can now be found on the Exercise page. |

10.05 | There have been some requests for a sketch of the solutions of exercise 5. It is on my todo-list, but not on the top of it. Hopefully, something appear in the beginning of next week. |

06.05 | The final curriculum and office hours before the exam can now be found at the end of this page. |

24.04 | The project and Exercise 5 is now graded. You can see the score and the comments at ovsys. |

01.04 | Exercise 5 can be found on the exercise page. |

01.04 | The presentation can be in English or Norwegian, of your own preference. English slides combined with a presentation spoken in Norwegian is also allowed. |

01.04 | On the project page you can now find information about when your group is to present you project. On Wednesday from 10:15 to 12:00, we will be in EL6 in Gamle elektro. In the lecture hours on Tuesday and Wednesday we will be in VE1, as usual. |

27.03 | Some information about the presentations of the project can be found on the project page. |

13.03 | On Wednesday March 20, 16:15-17:00 there will be a guest lecture by Vegard Berg Kvernelv (Norsk Regnesentral) with the title: Working as an industrial mathematician - How a maths degree is relevant six years later. The lecture will be in Norwegian. The tutorial this evening (March 20) is cancelled. |

05.03 | Exercise 4 can be found on the exercise page. |

05.03 | Wednesday 06.03, Andre Massing will give a guest lecture on Cut Finite Elements: How to solve real-world applications in engineering, biology and bio-medicine by cutting triangles. After his lecture, there will be some information about the project. |

03.03 | The projesct description and the list of PDEs is available (see the menu). |

20.02 | Exercise 3 can be found on the exercise page. |

07.02 | I and Sølve are both travelling next week. The lecture on Tuesday 12.02 will be given by Elena Celledoni. There will be no lecture or tutorials on Wednesday 13.02. |

07.02 | As agreed on, Exercise 2 has been updated with some hints for solving Problem 2b). If you still have problems with this exercise, I will be available in my office (1348, SBII) today (Thursday) and tomorrow 13:00-16:00. |

05.02 | Exercise 1 is graded. See your scores and comments in ovsys. |

29.01 | Exercise 2 is available at the exercise page. |

29.01 | I have to cancel the office hours (14:30-16:00) today. You are welcome any other days this week between 14:15 and 16:00. |

27.01 | All those who have sent an e-mail to Sølve should now be registered in a group in ovsys. You will see what group number you are registered in, but unfortunately not the other group members. Anyway, each group should submit their solution by one of the group members handing it in. |

24.01 | It is now possible to hand in the first exercise in ovsys. |

19.01 | The first exercise is out, se the under exercises/old exams in the menu. Deadline 28.01. The exercise counts can give up to 5 points for the final grade. |

16.01 | You should work in groups of two or three (ideally three) students on the exercises and project. Please send an e-mail to Sølve informing him of who is in your group, and he will register you in this group in ovsys. Also send an e-mail to Sølve if you want him to place you in a group with one or two other students. |

15.01 | There will be no exercise session this week (16.01). The first exercise will be available later this week. |

07.01 | The lectures have been moved to VE1 (Verkstedteknisk). |

03.01 | Welcome to TMA4212 TMA4212 Numerical solution of differential equations by difference methods. The first lecture is Tuesday 09.01, and the first exercise class Tuesday 15.01. |

09.01 | The exercise and project sessions will take place in Nullrommet. If you cannot enter here, please send an e-mail with your username, e-mail address and study programme to Abdullah. |

## Lecturer

Anne Kværnø, room 1348 Sentralbygg II,

Email: anne [dot] kvarno [at] math [dot] ntnu [dot] no (use TMA4212 in the subject heading)

## Exercise and project lecturers

## Lectures

- Tuesday 12:15-14:00, VE1 Verkstedsteknisk
- Wednesday 16:15-18:00, VE1 Verkstedteknisk

## Exercises

- Wednesday 10:15-12:00, Nullrommet

## Description of the course

In the following link you can find detailed information about the course, the main topics presented and the learning outcome.

## Learning outcome in itemized form:

Code | Description | |
---|---|---|

Knowledge | L1 | Understanding of error analysis of difference methods: consistency, stability, convergence of difference schemes. |

L2 | Understanding of the basics of the finite element method. | |

Skills | L3 | Ability to choose and implement a suitable discretization scheme given a particular PDE, and to design numerical tests in order to verify the correctness of the code and the order of the method. |

L4 | Ability to analyze the chosen discretization scheme, at least for simple PDE-test problems. | |

L5 | Ability to attack the numerical linear algebra challengies arizing in the numerical solution of PDEs. | |

General competence | L6 | Ability to present in oral and written form the numerical and analytical results obtained in the project work. |

L7 | Ability to apply aquired mathematical knowledge in linear algebra and calculus to achieve the other goals of the course. |

## Reference group

- Alexandra McEnroe, alexandra [dot] r [dot] m [dot] enroe [at] ntnu [dot] no, MSMNFMA
- Ellisiv Steen, ellisiss [at] stud [dot] ntnu [dot] no, MTFYMA

## Office hours before the exam (1348, SBII)

(May be subject to change)

- 10.05, 13:15-14:00
- 13.05, 14:15-16:00
- 14.05, 12:15-14:00
- 15.05, 10:15-12:00
- 16.05, 13:15-15:00

## Teaching material

- Note on finite difference methods by Brynjulf Owren
- Note on finite element methods by Charles Curry

#### Additional material

- J.W. Thomas: Numerical Partial Differential equations, Finite Difference Methods and Conservation Laws and Elliptic Equations
- J.C. Strikwerda: Finite Difference Schemes and Partial Differential Equations

## Curriculum

- The notes by Owren and Curry.
- Strikwerda, Chapter 13.1-3 and 14.1-3 (Linear algebra for PDEs).
- The exam questions listed in the Timetable.

It may also be an idea to look over the exercises once more.

## Exam info

The exam is 20.05, 09:00-13:00.

Permitted aids:

- Approved simple calculator
- The notes by Brynjulf Owren (finite differences) and Charles Curry (finite elements).
- Rottman

You are allow to mark/underline parts in the notes or in Rottman, but not to write anything in them.

**Evaluation system and marking in this course**

- There will be given 5 exercises, of which the best 4 each counts for up to 5 % of the final mark.
- The project counts for 20 % of the final mark.
- The final exam counts for 60 %. You must pass the final (written) exam to pass this class (project + homework + final exam).
- The total mark is the only official mark for the course. The marking of the project is unofficial.
- Exercises and the project can be done in groups, preferable of 2-3 students.