nonzero natural conditions in 1-D

I can’t figure out how to impose nonzero natural conditions on a one-dimensional problem.

Essential conditions are easy, same as in higher dimensions.

Consider u’’ = 0 with u(0) = 0 and u’(1) = 1 so that the exact solution is u = x.

I can solve this as trivially two-dimensional problem (∇v, ∇u) = [v, n . ∇u]|(x=1) = [v, 1]|(x=1):

m = MeshQuad.init_tensor(*(np.linspace(0., 1.),)*2)
e = ElementQuad1()
ib = InteriorBasis(m, e)
fb = FacetBasis(m, e)


@linear_form
def boundary_flux(v, dv, w):
    return v * (w.x[0] == 1.)


n = m.p.shape[-1]
L = asm(laplace, ib)
b = asm(boundary_flux, fb)
u, D = ib.find_dofs(lambda x, y: x == 0.)
I = ib.dofnum.complement_dofs(D)  # noqa E741
u = np.zeros_like(b)
u[I] = solve(*condense(L, b, I=I)) # noqa E741

but trying the same thing with the minimal modifications to drop the dimension from two to one

m = MeshLine(np.linspace(0., 1.))
e = ElementLineP1()

fails at FacetBasis with

NotImplementedError: The given mesh type is not supported!

I think that this is merely the proximate cause, raised by get_quadrature, but on inspection MeshLine appears incomplete, lacking attributes facets, t2f, f2t.

[kinnala]

I sort of saw these challenges when I reimplemented the 1D support but forgot to do anything about it. Let us try to find a fix so that the implementation is as similar as in higher dimensions.

[kinnala]

Closing this after adding some 1D tests.