Welcome to Math 692 Graduate Seminar: Finite Elements in Spring 2024! We are in the Dept. of Mathematics and Statistics at the University of Alaska Fairbanks.
- Course details:
- Organizer/Instructor: Ed Bueler, elbueler@alaska.edu.
- Time and place: Thursdays 3:30-4:30pm, Chapman 206. Please email me for the Zoom link. In-person is preferred if you are on campus!
- Credits (CRN 35370): 1.0, but non-credit attendance is welcomed.
-
The Github repo for this website has example codes in the
py/directory. - A schedule of topics is at the bottom. This schedule is subject to change!
guiding principles
- show up
- try stuff
content
My plan is to take the lead on this seminar, and do lectures at the start. Then to lead workshop style, encouraging student presentations, as much as possible.
We will cover the practical finite element method, through actual computations using Firedrake. I plan to mix in enough theory to make the code make sense. The goal is definitely not to prove systematically that the finite element method converges for certain problems.
An introductory partial differential equation problem is (of course) the Poisson equation. Then we can look at
- time-dependent problems like the heat equation,
- advection-diffusion equations,
- vector problems including the Stokes equations for fluids,
- nonlinear problems like the Liouville-Bratu equation,
- inequality-constrained problems like the obstacle problem, and any other models of interest to the participants.
topics (schedule)
| Date | Topic | Slides | Code in repo |
|---|---|---|---|
| 18 Jan | laptop day: install Firedrake, start Poisson | slides | code |
| 25 Jan | Poisson equation examples, Paraview | slide | code |
| 1 Feb | verification, assembly, errors | slides | code |
| 8 Feb | meshes & elements: Gmsh, P_k, Neumann | slides | code |
| 15 Feb | Stokes equations for glaciers | slides (ext) | code (ext) |
| 22 Feb | CANCELLED | ||
| 29 Feb | time-stepping | slides | code |
| 7 Mar | fast solvers for Poisson | slides | code |
| 14 Mar | Spring Break | ||
| 21 Mar | nonlinear problems and systems | slides slides |
code |
| 28 Mar | Stefano Fochesatto: obstacle problem | slides | code |
| 4 Apr | conservation and DG | slides FE table |
code |
| 11 Apr | Tara Shreve: porous media | slides (ext) | code (ext) |
| 18 Apr | Michael Christoffersen: linear elasticity | slides | code |
| 25 Apr | Austin Smith: waves | slides | code |