AMPS I · Week 10 — Time-Dependent Problems: θ-Method · Stability · Space–Time Convergence · Cahn–Hilliard

File What When
W10_lecture.html (.qmd source) Lecture slides — Parts A (theory), B (heat equation in DOLFINx), C (stability in practice), D (Cahn–Hilliard, LLM, HW9) in class
W10_lab.ipynb (Colab) Lab: θ-method loop with one factorisation, Gaussian benchmark, temporal rates and the spatial floor, explicit Euler limit and mass lumping, Crank–Nicolson oscillations and the Rannacher start, Cahn–Hilliard (energy, mass), LLM demo in class (≈ 80 min), finish at home
W10_HW9.ipynb (Colab) HW9 — amplification factor, 1D eigenvalues, energy stability; MMS with time-dependent boundary data: temporal rates, joint refinement, order reduction; explicit-Euler limit measured; LLM debugging due before Week 11
../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 9 lecture (closed-AI).

The Cahn–Hilliard cells of the lab take about a minute each on Colab.

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 — read every output before you submit.

Week 11 starts with a 10-minute quiz on this week’s lecture (closed-AI).