FEniCS-style bcs

[pbrubeck]

Description

With the default DirichletBC approach, the BCs are applied on the initial guess before linearising. This could be problematic, as the intial state with BCs could cause NaNs for some nonlinear problems containing functions that blow up like logarithms.

This PR adds a kwarg to solve(F == 0, u, bcs, pre_apply_bcs=False) to delay the imposition of bcs, so that the problem is linearised around the initial guess before imposing the boundary conditions. Internally, we assemble the residual of the bcs: bc_resid = u - bc_data on the rows of the residual Cofunction, and the rows and columns of the Jacobian remain as those of the identity, to preserve symmetry. This means that the interior rows of residual need an extra term F -= action(J, bc_resid) coming from the lifted BC values on each nonlinear update, in a similar way we already do for the BC lifting in the linear case.

A cool implication of this approach for nonlinear problems where the forcing is driven by inhomogeneous boundary conditions (inflow or traction BCs) is that a linesearch method automatically enables some sort of parameter continuation.

We also restore the old behaviour of zero_bc_nodes=False, so it no longer errors when we write primal data on a dual Cofunction boundary nodes, but zero_bc_nodes=True will remain as the default.

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake real	8079 ran	7366 passed	713 skipped	0 failed

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake complex	8150 ran	6594 passed	1556 skipped	0 failed

[JHopeCollins]

Please don't resolve comments with reviewer questions. The reviewer might still have questions/comments on that topic, and should be the one to decide if it is resolved or not.

[JHopeCollins]

Gusto and asQ tests all pass with this branch.

done