Implement IDP mortars for IDP limiting

[bennibolm]

Implementation of IDP-compatible AMR based on the idea of Dmitri Kuzmin.

[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

Attention: Patch coverage is 90.63604% with 53 lines in your changes missing coverage. Please review.

Project coverage is 96.72%. Comparing base (e1da2b6) to head (5d2152b).
Report is 10 commits behind head on main.

Files with missing lines	Patch %	Lines
src/solvers/dgsem_tree/containers_2d.jl	46.97%	35 Missing ⚠️
src/solvers/dgsem/basis_lobatto_legendre.jl	81.40%	8 Missing ⚠️
src/time_integration/methods_SSP.jl	53.85%	6 Missing ⚠️
src/solvers/dgsem/l2projection.jl	95.45%	2 Missing ⚠️
...llbacks_stage/subcell_limiter_idp_correction_2d.jl	99.33%	1 Missing ⚠️
src/solvers/dgsem_tree/dg_2d_subcell_limiters.jl	99.53%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2305      +/-   ##
==========================================
- Coverage   96.89%   96.72%   -0.17%     
==========================================
  Files         509      496      -13     
  Lines       41793    41476     -317     
==========================================
- Hits        40493    40117     -376     
- Misses       1300     1359      +59     

Flag	Coverage Δ
unittests	96.72% <90.64%> (-0.17%)	⬇️

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.