Remove extrapolated interpolation

[julianlitz]

The extrapolated interpolation based on triangular elements might not actually be necessary.
We could just use the standard interpolation operators instead and see slightly better error reductions.

Merge Request - GuideLine Checklist

Guideline to check code before resolve WIP and approval, respectively.
As many checkboxes as possible should be ticked.

Checks by code author:

Always to be checked:

• There is at least one issue associated with the pull request.
• New code adheres with the coding guidelines
• No large data files have been added to the repository. Maximum size for files should be of the order of KB not MB. In particular avoid adding of pdf, word, or other files that cannot be change-tracked correctly by git.

If functions were changed or functionality was added:

• Tests for new functionality has been added
• A local test was succesful

If new functionality was added:

• There is appropriate documentation of your work. (use doxygen style comments)

If new third party software is used:

• Did you pay attention to its license? Please remember to add it to the wiki after successful merging.

If new mathematical methods or epidemiological terms are used:

• Are new methods referenced? Did you provide further documentation?

Checks by code reviewer(s):

• Is the code clean of development artifacts e.g., unnecessary comments, prints, ...
• The ticket goals for each associated issue are reached or problems are clearly addressed (i.e., a new issue was introduced).
• There are appropriate unit tests and they pass.
• The git history is clean and linearized for the merge request. All reviewers should squash commits and write a simple and meaningful commit message.
• Coverage report for new code is acceptable.
• No large data files have been added to the repository. Maximum size for files should be of the order of KB not MB. In particular avoid adding of pdf, word, or other files that cannot be change-tracked correctly by git.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.32%. Comparing base (6787376) to head (d35d5f5).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #207      +/-   ##
==========================================
- Coverage   95.32%   95.32%   -0.01%     
==========================================
  Files          86       84       -2     
  Lines        9372     9318      -54     
==========================================
- Hits         8934     8882      -52     
+ Misses        438      436       -2     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[mknaranja]

I am not sure if this "might not be necessary". That could just reduce convergence order from 3 to 4 to 2.

[julianlitz]

For extrapolation we assume that the finest mesh is obtained from a single uniform refinement of the next coarser mesh.

The extrapolated prolongation currently sets the new value as

0.5 * [top_left + bottom_right]

while the standard prolongation would use

0.25 * [bottom_left + top_left + bottom_right + top_right].

I didn't notice any changes in the convergence orders. Rather ever so slightly better convergence, but not really noticeable.

So I was wondering if the extrapolated interpolation is straight up not necessary.

@mknaranja

[julianlitz]