Overview of lectures

Before the next group session we will create a repository for you in this course. If you have any questions about this or the course in general please send an email to inf5620@gmail.com.

Exercises 10, 11, 12; PDF p. 84. Solveig went thought Exercise 10.

Aug 28: 0815-0900: Basic discretization of diffusion equations; PDF; slides (Forward/Backward Euler and Crank-Nicolson schemes). 0915-1000: Quick overview of the finite element method. See handwritten notes.

Sep 2:

• Exercises 10, 11, 12; PDF p. 84. Note that Exercise 10 is extended to a time-dependent term and that Exercise 11 has more subexercises about verification techniques. Solutions: Exercise 10, Exercise 11 (cooling.py), effect of bugs in Exercise 11, detective.py.
• Exercises 1, 2; PDF p. 49. Solution: Exercise 1.

Sep 4: Introduction to finite element methods; PDF; slides. Covered the material until finite element basis functions.

Sep 9: Finite element basis functions, PDF p. 31, slides.

Sep 11: Everyone should solve Exercise 4, and 6 in the Introduction to finite element methods chapter; page 84 in PDF (note that the exercises were recently slightly changed, so if you have a printed PDF, check the online versions for updates of the exercises). Add the exercises to your GitHub repo. Groups of three will review three exercises. We call this compulsory exercises with peer review, and each student needs to participate in three events of this type. This is the first event. We will also do Exercise 5 and 7, but these are optional and not compulsory.

Sep 16: More about the finite element machinery, we start where we left off: Assembly of elementwise computations; PDF page 44; slides. We finished the chapter on approximation, incl. 2D/3D finite elements.

Sep 18: We add boundary terms to make the boundary values correct in Exercise 6. Some demonstrations of movies (Exercise 7) are shown to illustrate the effect of different choices of basis and the influence of boundary terms. This took 30 min. We continued with what was set up for Sep 23: Exercise 10 and 11 (page 88 in PDF). Thereafter, a quick overview of the wave equation project was given. The details of this project and background material to read will appear on this page very soon.

Sep 23: Solveig and Aslak will show up and be oracles for the exercises 13, 14, and 15, which are to be completed by Thursday. They can help you out with the finite element method as well as technical problems with Python programming or Git and GitHub. Take a look at the checklist for peer review of exercises to see the various points you should consider when solving (and later judging) an exercise.

Sep 25: Everyone should solve Exercise 13, 14, and 15 in the Introduction to finite element methods chapter (page 88 in PDF). The exercises must be pushed to your personal Git repository at GitHub in the INF5620 virtual classroom. The students will be divded into groups of three to perform peer review of the solutions by three other students. This is the second such session, and we require each student to participate in at least three such sessions during the semester (there will be 3-4 more - at least). Each group can use a checklist to see what should be considered when reviewing exercises.

Sep 30: Students are encouraged to show up in the Shell room and collaborate on the compulsory wave project.

Oct 2: Same as for Sep 30.

Oct 7, Oct 9: There will be lab with teaching assistant(s) available.

Oct 14: Students are divided into groups of three for assessing the compulsory wave project.

Oct 16: Ordinary lecture again on Basic principles for approximating differential equations; PDF page 92; slides.

Oct 21: We continue where we left and proceed with finite elements for solving differential equations.

Oct 23: Exercises to be handed in on GitHub and assessed by other students in groups of three: 18, 19, 24. Optional exercises: 20 and 16 can be assessed by the lecturer (hpl@simula.no). Some of these exercises have recently been (slightly) reformulated so make sure you check out the version from Oct 16 or later.

Oct 28: Ordinary lecture: Methods for incorporating nonzero Dirichlet conditions; PDF p. 119-142; slides. 2D/3D problems and time-dependent problems; PDF p. 143; slides.

Oct 30: Oracle 0815-1000: you can ask about exercises for next Tuesday.

Nov 4: Students meet and exchange exercises for assessment in groups of three. Exercise 26 and 27, plus a finite element wave equation project a)-f). We will do the analysis in g)-j) later. Make sure you are on time! (It requires extra manual work with the repositories to take care of students who show up too late.)

Nov 3: The text in the finite element wave equation project has been slightly adjusted to clarify numbering of nodes and unknowns and align the notation with the latest version of the course notes.

Nov 5: A default problem for the next compulsory project has been published.

Nov 6: Lecture on numerical methods for nonlinear differential equations. The notes have been rewritten and are not yet in their finished form, but major modifications will happen from Section 5 and onwards. It is recommended to read the notes and slides on the screen and print them next week. See link to electronic notes, PDF, and slides.

Nov 11: More about nonlinear ODEs and PDEs. We continue with Picard and Newton methods at the differential equation level; PDF p. 23; slides. The textbook material is in a quite good shape now and will not be changed (except for typos). Slides are also finished.

Nov 13: Brief info on application of Picard and Newton methods to 2D/3D variational forms and finite difference schemes.

Nov 13: Brief mentioning of generalizations of Picard and Newton methods to 2D/3D variational forms and finite difference schemes. Accuracy and stability analysis of finite difference schemes:

1. Vibration ODE (see also text, "PDF": "" p. 14)
2. 1D wave equation (see also text, "PDF": "" p. 50)
3. 1D diffusion equation (text, PDF p. 12)

Nov 18: Lecture 1015-1100. 1115-1200: Oracle for exercises about nonlinear problems.

Nov 20: Peer review of exercises for nonlinear problems. Make sure you deliver your files in Git on Nov 19. Exercises: 1, 4, 7, 8, 14, 16.

Nov 24: Deadline for final compulsory project.

Nov 25: Peer review of final compulsory project.

Nov 27: 0915-1000: Presentation and discussion of this year's exam. Because of a technical problem, this announcement didn't appear in UiO's Vortex pages before late Wednesday night, so we will repeat the session on next Thursday.

Dec 2: No lecture.

Dec 4: Peer review of points g)-j) in the project a finite element wave equation project. These points are highly relevant for this year's exam. We will also answer problems related to the exam.