I wanted to use MappingManifold for sphere, but it looks like this is not
possible either with PolarManifold or SphericalManifold.
I am doing this for a shallow water model on sphere, where I want to do
long time integration, and look at conservation of mass, energy, etc.
Having an exact mapping is important for conservation.
If I use *SphericalManifold + MappingQ*, I seem to have loss of mass
conservation over long time integration. In this case, can you tell me
about these questions ?
(1) If phi_i are the basis functions, does grad(phi_i) lie exactly on the
sphere ? (I guess not)
(2) If (x_q,y_q,z_q) is some quadrature point, is
sum_i grad(phi_i(x_q,y_q,z_q)) = 0
upto machine precision ?
The last property is necessary for mass conservation in DG schemes for
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