TMA4212 Numerical solution of differential equations by difference methods

The retake exam in August will be an oral exam. The exam will not take place on the 5th of August. To those of you who will take the exam, please get in contact with me at the beginning of August. Further information about the exam will be posted on this webpage or e-mailed directly to the students who kindly have contacted me via e-mail in due time. The oral retake exam will take place after the 10th of August. This will depend on the avilability of the students involved, of the external examiner and mine.
Allowed aids at the exam (official from the exam paper): "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."
Teching material allowed at the exam: book by Suli and Mayers, book by Strikwerda, the official note of the course.
The minutes of the last meeting with the reference group are now posted on It's learning.
This is a list of "easy" exercises that you can find in the book by Strikwerda. Exercise 1.4.1 and 1.4.2 p. 28 (read first the example 1.4.3). Exercise 1.5.1 p 33.
Project grades are available on It's learning.
A meeting with the reference group has been held on Tuesday the 17th of March. You can read the minutes from this meeting in It's learning. The next meeting will be held on the 4th of May, please give your input and comments to the members of the reference group if you suggestions on issues and topics that the reference group should address.
Information about the project report and code: 1) please use your candidate number on the report (no names, no student numbers); 2) the max number of pages in the report is 10; 3) use an appendix if you have some extra material you absolutely need to attach to the report, for example extra pictures or pseudo-code (but be advised that we will probably not read through the appendix); 3) the code should be submitted together with the final report, you can send multiple files BUT it should be easy enough for us to run the code (make a README file with the instructions of how to run the code and be careful with compression of files, we do not want toubles when uncompressing your files). The code will be used if we need to check parts of the report that we do not understand and in order to see how efficient is your implementation. Nice code contributes positively to the final score; 3) in the conclusion if the members of the group agree that the work has been distributed evenly, than you do not need to specify what each memeber of the group has done, write simply that each of the group members has contributed equally to the project work.
There will be no lecture Monday March 9th and Friday March 13th. Anders will be available at Nullrommet 15:15-17:00 on Monday and 09:15-11:00 on Friday.
Send me your presentations by March 16th 12:00, so that they are all on one computer and we do not waste time to upload presentations between each group.
Our plan is to organize all presentations on the 16th of March between 15:00 and 19:00. Prepare a power-point or beamer presentation on the work of your project. You will have 9 minutes to present your work, 3 minutes per person, and finally threre will be a short round for questions, including suggestions and recommendations from Anders and Elena. You will then have the week from the 17th to the 23rd of March to finish the writing of the project and to fix any mistakes or shortcomings. Notice that the quality of our suggestions to improve your project will depend on the quality of your presentation.
Remember that in the conclusion section of your project report it should be clearly stated what was done by who.
IMPORTANT: every group should meet at least ONCE with Elena or with Anders. This should happen VERY SOON (this week). All members of the group should participate at the meeting. Remember also that you are asked to give a statement in your report about how much you have contributed individually to the project.
Instead of lecture there will be project work in Nullrommet on Friday 27.02.
The minutes from the reference group can be found in It's learning
You can now find some codes implementing the solution of two BVP, the Crank-Nicolson method for the heat equation, the semi-discretization of the KdV equation and the one-way-wave equation under Exercises. Examples of how to compute and plot errors are also given.
Please take some minutes to answer to the survey organized by the reference group.
Theory exercises: a list of relevant execises for each chapter is available on the webpage under "Timetable" last column to the right. Elena and Anders will be available to answer to your questions on exercises mostly after Easter (we prefer to give priority to the project at the present time of the semester). Send us an e-mail to schedule an appointment.
IMPORTANT: every group should meet at least ONCE with Elena or with Anders to discuss the project work. ALL members of the group should participate to this meeting. We want to know how you are doing, what you chose and how you will proceed. To meet with Elena: I'm lecturing on Mondays (15-17) and Fridays (8-10), I can meet with you every day from the 17.02 to the 24.02 and form the 02.03 to the 06.03. (I'm often but not always in my office, if you want to be sure send me an e-mail before coming.)
There will be an extra exercise session on Wedensdays from 14:15-16:00. Office hours are updated.
The lecture 26.01 is cancelled. The exercise session 26.01 is rescheduled to 15:30.
From Monday 12.01 the lectures will be in VE 1
First lecture 5th of January 2015 15:15-17:00 in B1
Important dates
First lecture: Monday 5th of January 2015.
Choose the PDE for the project: 31st January 2015
Presentation of the project: 16.03 (room 1329 Sentralbygg II) time: 15:00-19:00
Project deadline: 23.03.2015


VE 1 Verkstedteksnisk 2nd floor (Auditorium 205) Monday 15:15-17:00, and Fridays 8:15-10:00

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.


Elena Celledoni, room 1346 Sentralbygg II.

Exercise and project lecturer

Anders Samuelsen Nordli, room 1050, Sentralbygg II.

Reference group

  • International master students: Luca Fenzi e-mail: lucafe (at)
  • Industrial mathematics: Olav Ersland e-mail: olaversland (at)
  • Industrial mathematics: Svend-Peder Oseth e-mail: svendpeo (at)

Office hours

Office hours for Anders during the project:

Day Hour

Please note that the office hours might be changed. Let me know if these times don't suit you.

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 12th 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 three tasks (implementation, analysis and efficiency) which can be viewed as three 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

Evaluation system and marking in this course
  1. 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.
  2. You get credit only for project work made during this semester.
  3. 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.
2015-07-19, Elena Celledoni