Course page for Mek4250 / Mek9250
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Exam is June 10.
There will be six topics. Four of the topics will be the same
as the first four topics of
the exam from 2023 .
There will further be two topics taken from Chap 3 and 9 but these are not
written yet.
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Course page from 2023
A lot of the material, exercises will be the same as in 2023. Hence, for now, in order to get a complete picture of the
course, have a look there.
Mandatory Exercise
- The mandatory exercise is here .
- Some notes regarding WSS can be found here
Reading material
-
Book
- Jan 22: Chap 1 updated. Halfway through Chap 2.
- Jan 25: updated Chap 2 and 3.
- Feb 3: updated Chap 3.
- Feb 9: various small updates thanks to Mehdi.
- Feb 11: tried to fix the many inconsistencies between v and w in chap 4.
- March 3: many updates to the first chapters - also two new chapters
- April 18: Chap 3, 9 updated.
- Review on numerical methods for Navier-Stokes equations.
Weekly schedule (will be updated as we go)
- First week: Chapter 1 in the book. Hand-written notes
- Second week: Chapter 2, Exercise 1.1-1.4 in Chap 1. notes based on Chap 2.
- Third week: Chapter 3, Exercises in Chap 2. notes based on Chap 3.
- 4. week (starting Feb 10) : Finnish Chap 3 and start on Chap 4. Exercise 3.1 - 3.5. Notes.
- 5. week (starting Feb 17) : Finnish Chap 4 (ie convection-diffusion ). Exercises 4.1-4.4. Notes.
- 6. week (starting Feb 24) : winter holiday
- 7. week (starting March 3): Start on Chap 5, the Stokes problem. Exercise this week is cancelled.
will be spent on this review) notes .
- 8. week (starting March 10): Jørgen Dokken will show us the magic of FEniCSx.
He will go through the tutorial .
Exercises on March 12 is an Q&A session for the mandatory exercise.
- 9. week (starting March 17): Start on the following review of methods for Navier Stokes equations (a couple of weeks) Exercises on March 19. is cancelled.
notes and more notes
- April 8. Finalize the review on Navier-Stokes equations. No exercise April 9.
- April 15-16. Easter holiday. Note that there is an interesting talk in the Hans Petter Langtangen Seminar , Wed at 15:
- April 22. Basic FEM, Chap 3 updaetd April 18. Exercises for April 23 are 3.1-3.5.
- April 29, 30. Cancelled.
- May 6. Finalize basic FEM and start on alternative formulations (Chap 9). May 7, Exercises 9.1 and 9.2.
- May 13. Finalize Chap 9. May 14. PhD students present (from the first four topics in the 2023 exam above or
at topic decided together with the lecturer.). The rest of the Exam topics put out.
- May 20. PhD students present.
Background reading
Several of these books are available for downloads through the library.
- Braess, Dietrich. Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press, 2001. (perhaps the easiest read)
- Brenner, Susanne C., and L. Ridgway Scott. "Finite element multigrid methods." The Mathematical Theory of Finite Element Methods (2008): 155-173.
- Quarteroni, Alfio, and Alberto Valli. Numerical approximation of partial differential equations. Vol. 23. Springer Science & Business Media,
- Elman, Howard C., David J. Silvester, and Andrew J. Wathen. Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Oxford university press, 2014.