Should we use a composition for Monge-Ampere?

[joewallwork]

If we apply the same monitor function to an adapted mesh, does the code DTRT?

[joewallwork]

The question here wasn't sufficiently well formed for me to still understand what exactly was meant. Assuming that it is about "continuing" adaptation with a new Mover based on the adapted mesh from a different Mover, I don't think this really makes sense. See comment in #48.

If the question is about whether applying the same monitor function to two different (but topologically identical) meshes gives the same mesh then this is an interesting question. I expect that the answer is no because there are many ways that the mesh can be moved and the Monge-Ampere approach is just one "choice". In fact, since it's based on optimal transport theory, the origin mesh is "baked in" because it's all about moving the mesh with minimal "effort" (in some sense). However, it's plausible that we could add an extremely simple test (with one free DoF, say) to test this.