Preparation for the next release

[kinnala]

• Fixes ElementTriDG.dofnames is incorrect #737
• Add ElementTriSkeletonP0 and ElementTriSkeletonP1
• Add HDG example 40
• Add mixed mesh example 41
• Fixes Add TrilinearForm #733
• Fixes mixed meshes #412 (only linear elements, remaining work: high order elements)
• Support a list of bases in asm()
• Add ElementHexDG
• Fixes Assemble inverse #672
• Add periodic mesh example 42

[kinnala]

[kinnala]

[kinnala]

Again a quite large PR (sorry for that) but @gdmcbain if you have any general suggestions I'm happy to hear those.

[kinnala]

Oh, one thing that's missing is a test for #733.

[gdmcbain]

On demonstrating and testing the TrilinearForm #733, I wondered when I first heard about it whether it would be applicable to the Newton-linearized linear and bilinear forms arising from the trilinear advective term in the Navier‐Stokes equations.

scikit-fem/docs/examples/ex27.py

Lines 66 to 67 in 5c4c2b1

	@LinearForm
	def acceleration(v, w):

scikit-fem/docs/examples/ex27.py

Line 80 in 5c4c2b1

return np.einsum('j...,ij...,i...', w['wind'], grad(w['wind']), v)

scikit-fem/docs/examples/ex27.py

Lines 83 to 84 in 5c4c2b1

	@BilinearForm
	def acceleration_jacobian(u, v, w):

scikit-fem/docs/examples/ex27.py

Lines 97 to 98 in 5c4c2b1

	return dot(np.einsum('j...,ij...->i...', w['wind'], grad(u))
	+ np.einsum('j...,ij...->i...', u, grad(w['wind'])), v)

but I haven't looked into it.

[gdmcbain]

One thing that might be good soon is an example demonstrating spatial periodicity. #688 Though there is already tests.test_manufactured.test_periodic_mesh_assembly.

[kinnala]

On demonstrating and testing the TrilinearForm #733, I wondered when I first heard about it whether it would be applicable to the Newton-linearized linear and bilinear forms arising from the trilinear advective term in the Navier‐Stokes equations.

Probably yes but it's a bit unclear to me when and how the sparse 3-tensor contraction can be done efficiently. See #733 and the linked discussion for more info. However, I can see that for some dimensions this can be a feasible approach. In UQ I think you may have a huge number of material fields already in the beginning, e.g., if doing Monte Carlo.

[kinnala]

@gdmcbain I used your example almost verbatim. I hope you don't mind.

[gdmcbain]

Sure. It's simple and gives an immediate visual display of periodicity.