I added simplified Landlab and FEniCSx soil-creep participants.

The simplified Landlab implementation is standalone and exposes the inner workings of Landlab for this specific example. It produces the same results as the Landlab implementation without depending on it.

Landlab uses a finite-difference method, while FEniCSx provides a finite-element alternative. The FEniCSx participant solves the same soil-diffusion equation as the Landlab participant, but uses a triangular mesh instead of Landlab's regular grid and backward Euler instead of Landlab's forward Euler time integration.

The Landlab and FEniCSx participants produce similar results with uni-directional coupling, but diverge under bi-directional coupling due to the differences in spatial and temporal discretization. These are the resulting FEniCSx plots, showing the visible differences from Landlab:

The discrepancy is caused by the influence of the soil-creep participant on the grass map in the bidirectional coupling. The grass, which determines the diffusivity of the soil creep, is limited by soil depth from the soil-creep participant based on the minimum soil-depth threshold. If soil depth at a cell is below the threshold, a grass patch that is fully grown will be reset.

Because the Landlab and FEniCSx implementations use different spatial and temporal discretizations, one participant can cross the minimum soil-depth threshold earlier than the other. The grass can therefore be limited in one simulation while remaining fully grown in the other.

Once the grass maps begin to differ, their evolution also diverges because the wolf-sheep-grass ABM participant is stochastic. The grass map starts getting limited in the FEniCSx-coupled simulation once the soil depth falls below the threshold.

After four steps, a fully grown grass patch is reset for the first time, and the Landlab and FEniCSx simulations begin to diverge.

TODO: Summarize and motivate the changes, link to issues, remove the checklist entries that are not relevant.

Checklist

• I added a summary of any user-facing changes (compared to the last release) in the changelog-entries/<PRnumber>.md.
• If I changed requirements.txt files, I regenerated sibling requirements-reference.txt files with python3 tools/releasing/update-requirements-reference.py (pass a path to update only that directory, or --all to refresh everything).

For new tutorials or tutorial cases:

• I followed the tutorial folder structure
• I added/updated the tutorial README.md
• I added/updated the tutorial metadata.yaml
• I added tests in tests/tests.yaml
• I submitted a pull request to the website with:
  • An entry in _config.yaml
  • A sidebar entry
  • An entry in the tutorials overview