Enforcing strong boundary conditions in petrov-galerkin methods

[colinjcotter]

When computing hydrostatic pressure, the test space is different from the trial space but (if the boundary conditions are correctly set) then the system is still solvable.

See: tests/extrusion/test_extrusion_hydro.py in the hydrostatic branch.

[wence-]

Did we agree that this is a problem, but not one we should carry an issue around for? Basically, the problem is that if the test and trial spaces are different it's a little difficult to see what one should do to the assembled system.

[funsim]

Did we agree that this is a problem, but not one we should carry an issue
around for? Basically, the problem is that if the test and trial spaces are
different it's a little difficult to see what one should do to the
assembled system.

Why? In coupled systems you can still end up with a square, invertible
matrix even if the test and trial spaces of the variational forms are
different.

[wence-]

To eliminate the appropriate variables from the test and trial spaces is non-trivial. Given a boundary condition on the trial space, we need to determine which dofs in the test space it kills (and vice versa).

[wence-]

Is it possible that this will be addressed by David's upcoming "geometric" BCs?

[colinjcotter]

It might be!

[dham]

I think this doesn't happen "for free". But I think it might easily be done.