# TMA4212 Numerical solution of differential equations by difference methods

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A document containing the material on 2D finite elements for the Poisson equation is available on It's Learning |

Allowed aids at the exam. Code C: Approved simple pocket calculator is allowed. The text book by Strikwerda, the book by Süli and Mayers, and the official note of the TMA4212 course (98 pages) are allowed. Photo copies on 2D finite elements (4 pages) are allowed. Rottman is allowed. Old exams with solutions are not allowed. The books in printed version are also allowed. |

Some solutions to old exam problems have been unavailable for a time. They are now available again. So is the exam and solution from last year. See "Old exams" in the menu. |

To hand in the project, send your report (in PDF, please) and Matlab (or Python) files by e-mail to Sølve within the deadline, 6th of April. Remember to include instructions on how to run your program. |

The order of the project presentations is now posted here. |

The project presentations on Tuesday will be divided into two session: The regular time in S3 and from 14:15 in the lunch room at the 13th floor of Sentralbygg 2. Those of you who are unavailable at 14:15 should send an e-mail to Sølve, and then your group will be scheduled for the first session. A schedule for all the groups will be posted on Monday. You should prepare a presentation for a maximum of 8 minutes, not including time for questions and comments. Important: Send your presentation by e-mail to Sølve by 09:00 on Tuesday. |

Elena and Sølve will be away the last three days of this week, and are thus unavailable in the office hours on Thursday 2nd. Jon Vegard will supervise the project work on Wednesday 1st and Friday 3rd, at Nullrommet. |

The extra exercise session Friday 10th at 10:15-12:00 will be in Nullrommet. |

Homework 2 has been corrected, visit https://ovsys.math.ntnu.no to see if your has been approved. Many of you had problems with this exercise. We urge you to read through the comments here, and see if they address the problems you encountered. |

Important: The deadline for registration for the project was yesterday. If any students have not registered in the registration form yet but plan to do the project, you should register immediately! Note that the project counts for 35% of the final mark, so if you do not participate, you will need to have everything correct on the final exam to get a C. |

Since many students seem to have trouble with the initial deadline for Exercise 2, we have moved it to Friday. Hence you could ask Sølve in the exercise session on Wednesday if you still have questions on this exercise. You should also check the Homework page, where additional comments have been added. |

Homework 1 has been corrected, visit https://ovsys.math.ntnu.no to see if your have been approved. Under Homework, you will find a list of the most common errors. You should check if any of these apply to you. |

Please volunteer for being part of the reference group. |

Note: If you don't have access to Matteland, you need to send your full name, NTNU username and the card number on your student identity card to Sølve as soon as possible. |

Important dates |
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First lecture: Tuesday 10th of January 2017. |

Choose the PDE for the project: 1st of February. |

Presentation of the project: 28th of March. |

Project deadline: 6th of April. |

## Lecturer

Elena Celledoni, room 1346 Sentralbygg II.

## Exercise and project lecturer

Sølve Eidnes, room 1356, Sentralbygg II.

### LECTURE ROOM

S3 Tuesdays and R10 Fridays 10-12

Nullrommet, 3rd floor, central building 2 (Sentralbygg 2), Wednesdays 16-18

## Calendar

## 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. |

### Weekly work plan for this course to achieve these goals

Lectures | Assignments and Project supervision | Self study |
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4 hours | 2 hours | 6 hours |

## Reference group

Mira Lilleholt Vik **e-mail:**miralv (at) stud.ntnu.no

Gina Magnussen **e-mail:** ginama (at) stud.ntnu.no

Max Kieler **e-mail:** mfkieler (at) stud.ntnu.no

Kristoffer Skuland **e-mail:** krisskul@stud.ntnu.no

## Office hours

Office hours for Sølve and Elena:

Day | Hour | |
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Elena | Thursday | 14:15-15:00 |

Sølve | Thursday | 10:15-11:00 |

Please note that the office hours might be changed.

## 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** starting from the 17th 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 divided in two tasks (implementation and analysis) which can be viewed as two separate exercises. Refer to the official description of the course for the requirements on project/exercises relative to the exam. 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 course note (updated Jan 31st 2017) 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 exercises count for 5% the final mark and are compulsory.
- The project counts for 35 % 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).
- You get credit only for project work and exercises 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).