Rename derivative_dhat => derivative_hat, explain minus signs

[DanielDoehring]

$D$ is the abbreviation for the derivative matrix, so derivative_dhat is somewhat doubled - we also do not have derivative_dsplit but only derivative_split:

Trixi.jl/src/solvers/dgsem/basis_lobatto_legendre.jl

Lines 30 to 33 in b08f7da

	derivative_matrix::DerivativeMatrix # strong form derivative matrix
	derivative_split::DerivativeMatrix # strong form derivative matrix minus boundary terms
	derivative_split_transpose::DerivativeMatrix # transpose of `derivative_split`
	derivative_dhat::DerivativeMatrix # weak form matrix "dhat",

Furthermore, I compressed boundary_interpolation to the only two retrieved values. I think this is fine since the stored boundary matrix is currently also not the full one.

I also added a couple comments on the (minus)-sign in the construction of the matrices.

[github-actions]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• The PR has a single goal that is clear from the PR title and/or description.
• All code changes represent a single set of modifications that logically belong together.
• No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• The code can be understood easily.
• Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• There are no redundancies that can be removed by simple modularization/refactoring.
• There are no leftover debug statements or commented code sections.
• The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

• New functions and types are documented with a docstring or top-level comment.
• Relevant publications are referenced in docstrings (see example for formatting).
• Inline comments are used to document longer or unusual code sections.
• Comments describe intent ("why?") and not just functionality ("what?").
• If the PR introduces a significant change or new feature, it is documented in NEWS.md with its PR number.

Testing

• The PR passes all tests.
• New or modified lines of code are covered by tests.
• New or modified tests run in less then 10 seconds.

Performance

• There are no type instabilities or memory allocations in performance-critical parts.
• If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

• The correctness of the code was verified using appropriate tests.
• If new equations/methods are added, a convergence test has been run and the results
  are posted in the PR.

Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.02%. Comparing base (19f769d) to head (15cdf0c).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2725   +/-   ##
=======================================
  Coverage   97.02%   97.02%           
=======================================
  Files         563      563           
  Lines       44222    44225    +3     
=======================================
+ Hits        42904    42907    +3     
  Misses       1318     1318           

Flag	Coverage Δ
unittests	97.02% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ 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.

[DanielDoehring]

@jlchan we can also postpone the boundary stuff and just focus on the derivative matrix (as the title suggests 🙊 )

[jlchan]

I'm OK with the Dhat change if you want to just do that refactoring first. It might also be good to get one more review since this PR touches a lot of code

[jlchan]

Thanks for removing the boundary stuff. One minor comment on your comment

[ranocha]

Why did you remove this comment?

[DanielDoehring]

I found that improvement pretty trivial/obvious. And to prevent comment overload decided to remove that.

[DanielDoehring]

I found that pretty trivial/obvious improvement and to prevent comment overload decided to remove that

[ranocha]

Ok, thanks