Arbitrary Precision LGL Basis

[DanielDoehring]

Convergence study:

####################################################################################################
l2
scalar              
error     EOC       
1.23e-16  -         
9.88e-18  3.64      
6.55e-19  3.92      
4.20e-20  3.96      
2.70e-21  3.96      
1.69e-22  4.00      

mean      3.90      
----------------------------------------------------------------------------------------------------
linf
scalar              
error     EOC       
1.75e-16  -         
1.40e-17  3.64      
9.26e-19  3.92      
5.94e-20  3.96      
3.82e-21  3.96      
2.39e-22  4.00      

mean      3.90      
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("scalar",)
  :l2        => [3.89539]
  :linf      => [3.89539]

[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.

[JoshuaLampert]

I just had a brief look.

[codecov]

Codecov Report

Attention: Patch coverage is 95.91837% with 4 lines in your changes missing coverage. Please review.

Project coverage is 96.39%. Comparing base (50d30e9) to head (3295d6e).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/auxiliary/special_elixirs.jl	60.00%	2 Missing ⚠️
src/solvers/dgsem/basis_lobatto_legendre.jl	96.88%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2128      +/-   ##
==========================================
- Coverage   96.39%   96.39%   -0.00%     
==========================================
  Files         483      483              
  Lines       38320    38325       +5     
==========================================
+ Hits        36938    36941       +3     
- Misses       1382     1384       +2     

Flag	Coverage Δ
unittests	96.39% <95.92%> (-<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.

[sloede]

Not a full review but I like the PR - cool idea!

[ranocha]

Thanks a lot! Is this close to be ready from your point of view?

[DanielDoehring]

Thanks a lot! Is this close to be ready from your point of view?

The only open question from my side would be the issue with the analysis function, i.e., whether we want to use the current "hot-fixed" way.

[sloede]

Very cool feature! Just a small note, otherwise LGTM!

[torrilhon]

Please note #1880 ...

[ranocha]

Failing tests are not related to this PR, see #2185 (comment). Thus, I will merge this now. Thanks