# TMA4212 Numerical solution of differential equations by difference methods

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Good luck for the exam!! |

The solution of the exam June 2012 is now available. |

Note that exercise 2 in the continuation exam August 2012 is not part of the curriculum. But if you managed to solve it anyway, you did not waste your time, it means that you understood the material quite well! |

You are allowed to bring Rottmann (formel samling) at the exam. |

You can bring copies of the allowed books at the exam but make sure that they are bound in one piece to allow control. |

Allowed aids under the exam, code C: Approved simple pocket calculator. The tex book by Strikwerda, the book by Suli and Mayers, and the official note of the TMA4212 course (98 pages). Photocopies on 2D finite elements, 4 pages, (see It's learning) are also allowed. Rottmann is allowed. Old exams with solutions are not allowed. |

The project grades have been published on It's learning. If you want some more information on the evaluation of your group's project you can send an e-mail to Anders or Elena. You did a lot of work on these projects, and this is reflected in many very good grades. |

At the exam you are allowed to take: the pdf note of the course, the book of Strikwerda, the book of Suli and Mayers, and the file on 2D finite elements you find in It's learning. Old exams with solutions or other notes are not allowed. |

You will find on It's learning a pdf-file containing the material on FEM for 2D Poisson equation. |

Remember to write your candidate number on your report. Do not write your name. |

Purpose of the presentation: 1) You will get experience in presenting the results of a project to an audience (you can present in Norwegian or in English as you prefer, but if you speak English everybody will be able to understand you). 2) The presentation is a means for Anders and myself to learn about your effort and results in the project work, so that it will be easier for us to read and evaluate the reports. We will ask to each group how they experienced the collaboration with the other members of group. 3) In case we spot mistakes in what you have done, we will let you know under the presentation and you will have the chance to fix them before you hand in the report. 4) You will present your work to the class so that they can learn a bit more about your PDE and your methods. |

Information about the project presentation: The presentations will take place in H1 (Tuesday 1. April) and in R3 (Wednesday 2. April). Each group will have 15 min at their disposal divided as follows: 9 min for the presentation, 4 min for questions, 2 min for changing to the next group. Please make sure you hold the time. Please show up at 15:00 sharp on Tuesday and at 8:00 sharp on Wednesday to avoid time problems (this is very important especially on Wednesday, as we will have to leave R3 at 10:00). This is crucial for the first two groups on the list (see list here). Prepare a pdf file of your presentation and send it to us Tuesday 12:00 at the latest. We will put all files on a laptop which you will use for your the presentation. |

I have made a presentation schedule here. Please let me know if there is someone missing, or something wrong. Anders. |

On Wednesday 26th I will be in my office from 8:15 to 16:00 and you can come to ask questions about the project. I'll have lunch (and a meeting) between 12-13. If some important meetings come up I'll let you know, watch this space. |

After the presentation of the project, those who need more time to finalize their report can get it upon request (maximum one week). Please send a message about it to Elena or to Anders. |

Important message: on Monday 10th of March the lectres will be replaced with project supervision (Anders will meet you in Nullrommet form 14-16). On Tuesday 11th of March instead there will be a lecture with Elena in H1 from 15-17 which will replace the usual project supervision. |

Wednesday 26th of February supervision of the project instead of the usual lecture. Anders will help you with the questions you might have from 8:15 to 10:00 in Nullrommet 3rd floor sentralbygg II |

We had our first meeting with the reference group on Friday 14.02. A short summary will be soon published here. |

For those who do not access to NULLROMMET: please send me your name, NTNU username/e-mail address, as soon as you get it. |

A mistake has been corrected in the BVP (CASE 3 page 20) in the note of the course. |

Please volunteer as members of the reference group. |

Those stusents who do not have access to NULLROMMET should send me en e-mail with the following information: your name and NTNU-username/@stud.ntnu.no-email. |

Important dates |
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First lecture: Monday 6th of January 2014 14:15 to 16:00. |

Choose the PDE for the project: 19th of February |

Presentation of the project: 1st and 2nd of April |

Project deadline: 4th of April |

Supervision of the project in Nullrommet |
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Tuesday 18th of Feb. 15-17 |

Tuesday 25th of Feb. 15-17 |

Wednesday 26th of Feb. 8-10 |

Tuesday 4th of Mar. 15-17 |

Monday 10th of Mar. 14-16 |

Tuesday 18th of Mar. 15-17 |

Tuesday 25th of Mar. 15-17 |

Wednesday 26th of Mar. 8:15-16 |

## 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 | |
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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. |

## Lecturer

Elena Celledoni, room 1346 Sentralbygg II.

## Exercise and project lecturer

Anders Samuelsen Nordli, room 1050, Sentralbygg II.

## Reference group

**Benedicte Meløy Christensen** (Industrial Mathematics), email: benedicc (at) stud.ntnu.no

**Andreas Borgen Longva** (Industrial Mathematics ), email: andrebl (at) stud.ntnu.no

**Jonas Blomberg Ghini** (Energy and Environment), email: jonas.blomberg.ghini (at) gmail.com

## Office hours

Wednesday 10:15-11:00

## Exercises and project

The exercises and exercise classes in this course are mostly aimed at facilitating the work for the project. Both lectures and exercises classes are also a preparation to the exam (in terms of exam exercises).
The exercise classes make use of computers and will be held in **NULLROMMET**(sentralbygg 2, 3rd floor) starting from the 7th of January.

The project aims at developing experience in implementing and experimenting with finite difference discretizations of PDEs. This is the core of this course. It contributes to achive the following goals for the course: L1, L3, L4, L5, L6, L7. The project is compulsory (see official description). The project work is essential to achieve L3, L5, L6 (which is about 40 % of the learning outcome for the course). See the project description for more detalied information.

## Teaching material

- We will use for the first part of the curriculum the noteFeb242014 of the course. The note might be updated during this semester.
*Finite difference schemes and partial differential equations*, John C. Strikwerda, SIAM, (second edition).- Book by Süli and Mayers for the finite element method.

**Evaluation system and marking in this course**

- The project counts for 40 % of the final mark. The final exam counts for 60 %. You must pass the final exam to pass the exam (project + final exam). To pass the final exam at least 40% of the answers should be correct.
- You get credit only for project work made during this semester.
- The total mark is the only official mark for the course. The marking of the project is unofficial and will be published on
*It's learning*(in letter form: A,B,C,D,E,F). This mark cannot be referred to during a complaint.