AMPS I · Week 11 — Stokes Flow: Mixed Problems · Inf-Sup · Brezzi · Taylor–Hood, MINI and Unstable Pairs

File What When
W11_lecture.html (.qmd source) Lecture slides — Parts A (theory), B (mixed spaces in DOLFINx), C (element pairs in practice), D (LLM, HW10) in class
W11_lab.ipynb (Colab) Lab: mixed and enriched elements, Poiseuille exactness, Taylor–Hood MMS and the interpolant pitfall, two P1–P1 failures, discrete inf-sup constants, Stokes cavity and its symmetry, LLM demo in class (≈ 80 min), finish at home
W11_HW10.ipynb (Colab) HW10 — saddle-point theory and Fortin’s bubble; one solver for Taylor–Hood, MINI and P1–P1 (rates, pressure plot, cost); your own inf-sup computation; LLM debugging due before Week 12
../dolfinx_0.11_api_reference.md DOLFINx 0.11 API reference sheet — paste it into your LLM always

The session starts with a 10-minute quiz on the Week 10 lecture (closed-AI).

The inf-sup cells (lab §5, HW Q3) build dense matrices and run with -np 1; they take up to a minute.

Before submitting: Runtime → Restart session and run all, fill in the AI-usage log, download the .ipynb. An error inside a %%fenicsx cell does not stop Run all, and a singular Stokes matrix may still give KSP reason 4 — read every output and plot the pressure.

Week 12 starts with a 10-minute quiz on this week’s lecture (closed-AI).