Consider stabilization options

[agzimmerman]

In additional to stabilizing advection with something like SUPG, we may want to stabilize interior layers (primarily the phase interface) with some kind of shock capturing method.

[agzimmerman]

Here are a couple of nice places to start:

• https://www.researchgate.net/publication/309284120_Stabilised_dG-FEM_for_incompressible_natural_convection_flows_with_boundary_and_moving_interior_layers_on_non-adapted_meshes
• https://www.researchgate.net/publication/298800738_A_grad-div_stabilized_discontinuous_Galerkin_based_thermal_optimization_of_sorption_processes_via_phase_change_materials

[agzimmerman]

Also someone mentioned that the "continuous interior penalty" method might be good for the phase-change layer.

[agzimmerman]

Also how much could we gain just by using DG for the enthalpy equation? See issue #281

[agzimmerman]

This is also related to the idea of using HDiv elements. See issue #252

[agzimmerman]

In a way this could address issue #191.