# TMA4212 Numerical solution of differential equations by difference methods

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The solution to the exam is posted on It's learning. There was a sign error in the PDE of the last exercise. This affected the second part of the exercise and will be taken into account in the evaluation. |

The errors in the solution of the retake exam from 2011 have now been corrected. |

The concept of F-stability is NOT part of the curriculum. With the nomenclature Lax-Richmayer stability (mentioned in one of the exams) we mean the concept defined in chapter 5 section 5.6. |

With the help of some students I've found mistakes in the solution of the retake exam from August 2011 (exercise 2, on FEM). I'll try to make corrections and post the corrected version by tiomorrow. |

The project results are now available on itslearning. |

The old exams that do not have an available solution are not part of the syllabus. The exams from 2012 were based on a somewhat different syllabus with more focus on finite element methods than we have have this semester. |

Regarding the project work and the exam. If you have not handed in any report for the project work you have not fullfilled the lerning outcome L3 and L6. These are learning goals which constitute the core of this course. According to the official description of the course, the project work is mandatory. So you should not be able to take the exam without having handed in the project work. Trygve Bærland reminded me that there was some different information regarding this issue posted earlier on this webpage (hanging from old versions of this webpages). For this reason you'll be allowed to take the exam anyway. However, as I repeatedly emphasized during the whole semester, lacking L3 and L6 is a serious drawback for your future studies and career. I'll also appreciate that those who did not hand in the project work contact me, I'd like to discuss with you the reasons that induced you to make this choice. There was indeed a link to the official description of the course since the beginning of the semester. |

Office hours before the exam: Tuesday 21st 14:15-16:00, Wednesday 22nd 8:30-10:00. |

At the exam you should not forget to take with you the photocopies on 2D finite elements (see It's learning), at least chapter 13 and 14 of the book by Strikwerda, the chapter on finite elements from the book by Suli and Mayers. |

The items L3 and L6 of the learning outcome (see list below), have been tested in the oral presentation and will be tested in the evaluation of the reports. The evaluation of the reports is based on the guidelines described in semester project (under evaluation). In addition Håkon has made a more detailed set of gudelines specifying points for each of the tasks successfully completed by the students in the reports. The exam will be designed to test especially the items L1, L2, L4, L5, L7 of the learning outcome (see list below). |

The notes of the course have been updated. There were some inconsistencies in the notation regarding the local truncation error which now have been removed. |

Please do not put your names on the presentation you are sending us, but only your candidate numbers. |

The second report from the reference group and the photocipies regarding the last part of the finite element lectures are now available on It's learning. |

Since the presentation of the project work will be done with a projector and on a screen, you are allowed to prepare a power-point/bearmer presentation of your work if you like. As a rule of thumb you should not use more than 5, 6 transparencies. The poster-format is also OK. ALL presentations should be sent in to Håkon by e-mail in electronic version by Monday April 29th by 17:00. We will arrange the presentations on a laptop so that they can be displayed without too much loss of time. You will spend 5 minutes presenting your work and then there will be a quick round of questions. The groups 1 -10 should be prepared to present their work on the 30th in H1, we start at 8:15 and end this section at 10:00. The remaining groups on Friday 3rd in S1, from 14:15 to 16:00. If we are not able to keep the plan of the presentations, we will have to move some of the groups from Tuesday to Friday |

The 23rd and 26th of April instead of lectures we have project supervision. |

THE DEADLINE FOR HANDING IN THE REPORT ON THE PROJECT WORK HAS BEEN EXTENDED TO THE 26TH OF APRIL. THE PRESENTATION OF THE PROJECT WORK WILL TAKE PLACE BOTH ON THE 30TH OF APRIL AND ON THE 3RD OF MAY: CA 10 GROUPS EACH OF THE DAYS. |

I remind you that there is a possibility to express your opinion on the course in a blog in It's learning. Please, log in in It's learning and use a few minutes and think if you have something to say about the three topics of discussion proposed in the blog or other issues. Your opinion will be anonymous. |

## We have provided supervision for the project work on the dates

- March 5th 2013, from 8-10 (instead of the regular lecture)
- March 7th 2013, from 14-16 (instead of the regular lecture)
- March 14th 2013, from 14-15 (this time both Håkon and Elena were present at the supervision, and we used far more than one hour)
- April 5th 2013, from 14-16 (instead of the regular lecture)
- April 23rd, 8-10 and 26th, 14-16 (instead of the regular lecture, both Elena and Håkon were present and we used far more than two hours each time)

In addition, all Thursdays in March and April form 14-15 were devoted to supervision of the project work.

## Description of the course

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

### In this course you'll acquire:

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.

## Exercise and project lecturer

Håkon Marthinsen, room 1342.

## Reference group

**Trygve Bærland** (Industrial Mathematics), email: trygve.baerland (at) gmail.com

**Snorre Husby** (Industrial Mathematics), email: snorreal (at) stud.ntnu.no

## Office hours

Monday 2pm-3pm

## Semester project

This 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. If you decide not to work on the project we are unable to test if you have achieved L3, L5, L6 (which is about 40 % of the learning outcome for the course). Then your mark will be D or less. See the project description for more detalied information.

## Text book and other teaching material

*Finite difference schemes and partial differential equations*, John C. Strikwerda, SIAM, (second edition).- We will use the note of the course. The note might be updated during this semester.

**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.