First order finite volume 1D

[jmbender]

I enabled first order finite volume methods on the 1D TreeMesh. Therefore I modified Lobatto Legendre basis to allow polynomial degree zero and fixed the determination of cell midpoints. Last I modified the visualization to receive the right cell boundaries and added a test.

Here is the result of a convergence test

julia> convergence_test("examples/tree_1d_dgsem/elixir_advection_finite_volume.jl",7)
...
####################################################################################################
l2
scalar              
error     EOC       
1.17e-02  -         
5.75e-03  1.02      
2.75e-03  1.06      
1.38e-03  1.00      
6.86e-04  1.00      
3.41e-04  1.01      
1.71e-04  1.00      

mean      1.02      
----------------------------------------------------------------------------------------------------
linf
scalar              
error     EOC       
1.65e-02  -         
8.12e-03  1.02      
3.89e-03  1.06      
1.94e-03  1.00      
9.70e-04  1.00      
4.82e-04  1.01      
2.41e-04  1.00      

mean      1.02      
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("scalar",)
  :l2        => [1.01588]
  :linf      => [1.01559]

Here is a plot result

julia> trixi_include("examples/tree_1d_dgsem/elixir_advection_finite_volume.jl")
julia> plot(sol)

[ranocha]

Thanks a lot!

@sloede It would be nice to get a brief review from you since I was involved in this PR.

[ranocha]

This enables the functionality requested in #1318 on the 1D TreeMesh.

[codecov]

Codecov Report

Merging #1489 (4a2b660) into main (9bd246f) will decrease coverage by 0.04%.
The diff coverage is 40.91%.

❗ Current head 4a2b660 differs from pull request most recent head 24978ea. Consider uploading reports for the commit 24978ea to get more accurate results

@@            Coverage Diff             @@
##             main    #1489      +/-   ##
==========================================
- Coverage   95.70%   95.66%   -0.04%     
==========================================
  Files         360      360              
  Lines       29816    29835      +19     
==========================================
+ Hits        28533    28539       +6     
- Misses       1283     1296      +13     

Flag	Coverage Δ
unittests	95.66% <40.91%> (-0.04%)	⬇️

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

Impacted Files	Coverage Δ
src/visualization/types.jl	88.84% <13.33%> (-5.66%)	⬇️
src/solvers/dgsem/basis_lobatto_legendre.jl	88.85% <100.00%> (+0.14%)	⬆️
src/solvers/dgsem_tree/containers_1d.jl	97.33% <100.00%> (ø)
src/solvers/dgsem_tree/containers_2d.jl	96.32% <100.00%> (ø)
src/solvers/dgsem_tree/containers_3d.jl	97.65% <100.00%> (ø)

[sloede]

Overall this LGTM, I have only two small suggestions/questions

[sloede]

Thanks a lot for this contribution and for bearing with us in the review process. LGTM 👍