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]

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Created with ❤️ by the Trixi.jl community.

[JoshuaLampert]

I just had a brief look.

[codecov]

Codecov Report

Attention: Patch coverage is 96.00000% with 4 lines in your changes missing coverage. Please review.

Project coverage is 96.36%. Comparing base (e1950ac) to head (16abc04).

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   96.36%   96.36%   -0.00%     
==========================================
  Files         480      480              
  Lines       38069    38084      +15     
==========================================
+ Hits        36684    36697      +13     
- Misses       1385     1387       +2     

Flag	Coverage Δ
unittests	96.36% <96.00%> (-<0.01%)	⬇️

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[sloede]

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

[DanielDoehring]

14'th order convergence test (elixir_advection_float128.jl) :

####################################################################################################
l2
scalar              
error     EOC       
6.50e-09  -         
3.69e-13  14.10     
2.76e-17  13.71     
1.68e-21  14.00     
1.03e-25  14.00     
6.27e-30  14.00     
1.16e-31  5.75      

mean      12.59     
----------------------------------------------------------------------------------------------------
linf
scalar              
error     EOC       
5.36e-08  -         
3.06e-12  14.09     
3.26e-16  13.20     
2.00e-20  13.99     
1.24e-24  13.98     
7.55e-29  14.00     
2.19e-31  8.43      

mean      12.95     
----------------------------------------------------------------------------------------------------

8'th order convergence (elixir_advection_double_float.jl):

####################################################################################################
l2
scalar              
error     EOC       
6.81e-11  -         
2.63e-13  8.02      
1.03e-15  8.00      
4.01e-18  8.00      
1.57e-20  8.00      
6.12e-23  8.00      
2.39e-25  8.00      

mean      8.00      
----------------------------------------------------------------------------------------------------
linf
scalar              
error     EOC       
5.83e-10  -         
2.34e-12  7.96      
9.11e-15  8.00      
3.58e-17  7.99      
1.39e-19  8.01      
5.46e-22  7.99      
2.12e-24  8.01      

mean      7.99      
----------------------------------------------------------------------------------------------------

[ranocha]

Can we please collect an issue listing these differences between the TreeMesh and the StructuredMesh?