Add parabolic terms for P4estMesh{2}

[jlchan]

This PR implements (periodic) parabolic terms on curved 2D P4est meshes. There is currently a test for advection-diffusion. We haven't yet added a Navier-Stokes test because elixir_navierstokes_convergence.jl requires boundary conditions.

#1492 should be merged first to reduce the size of this PR. Additionally, boundary conditions will be implemented separately in #1493 to reduce the size of each PR.

[codecov]

Codecov Report

Merging #1490 (2b91590) into main (4f35801) will decrease coverage by 0.39%.
The diff coverage is 90.53%.

@@            Coverage Diff             @@
##             main    #1490      +/-   ##
==========================================
- Coverage   96.14%   95.75%   -0.39%     
==========================================
  Files         360      363       +3     
  Lines       29945    30183     +238     
==========================================
+ Hits        28788    28900     +112     
- Misses       1157     1283     +126     

Flag	Coverage Δ
unittests	95.75% <90.53%> (-0.39%)	⬇️

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

Impacted Files	Coverage Δ
src/solvers/dgsem_p4est/dg.jl	100.00% <ø> (ø)
src/solvers/dgsem_p4est/dg_2d_parabolic.jl	88.83% <88.83%> (ø)
...st_2d_dgsem/elixir_advection_diffusion_periodic.jl	100.00% <100.00%> (ø)
...gsem/elixir_advection_diffusion_periodic_curved.jl	100.00% <100.00%> (ø)
src/solvers/dgsem_tree/dg_2d_parabolic.jl	94.92% <100.00%> (ø)

... and 6 files with indirect coverage changes

[jlchan]

Thanks @sloede and @efaulhaber for the reviews! I've addressed the points raised.

[jlchan]

Oops, didn't see this comment @sloede

I haven't done a check of the implementation logic but only looked at the syntax (which looks fine). Have you been able to show the expected EOC when running convergence tests with both new elixirs?

I haven't tested this yet, but I plan to add it in the boundary condition PR.

Also, coverage is not optimal since the boundary condition code is mostly unused - am I right to assume that this will be added in a subsequent PR?

Yep, in #1493

[sloede]

LGTM (but please wait for @efaulhaber for the 🟢 )

[efaulhaber]

All looking good now. Math makes sense 👍

[jlchan]

@sloede your old review was wiped when I added some commits. Mind approving again?

[efaulhaber]

Or does it make sense to add a comment to that part? Maybe just a reference to the corresponding discussion here, where we explained everything in proper formulas?

[jlchan]

Or does it make sense to add a comment to that part? Maybe just a reference to the corresponding discussion here, where we explained everything in proper formulas?

Good idea. Added in 8956587

[jlchan]

The coverage drops prevent this from merging. The drop in coverage is from the boundary condition stuff, which we'll add in #1493.

[ranocha]

Ok