Failing convergence in nonlinear solve

[Martin Sandve Alnæs]

Reported by Gabriel Balaban

#!/usr/bin/env python
from dolfin import *

#Turn this on or off to make the Newton solver converge / diverge.
parameters["form_compiler"]["representation"] = "uflacs"

m = UnitSquareMesh(2,2)

V = VectorFunctionSpace(m, "CG",1)
u = Function(V)
v = TestFunction(V)

F = inner(grad(u),grad(v))*dx + inner(as_vector((0.001,0)),v)*dx
solve(F == 0, u)

[Martin Sandve Alnæs]

This is weird, considering that assemble(F) and assemble(derivative(F,u)) returns exactly the same vector and matrix with standard ffc and uflacs.

[Martin Sandve Alnæs]

Set representation to "quadrature" and you get the same result.

But is this really supposed to converge? I found that assembling F with u= a large constant gives slightly different results for tensor representation, but F only depends on the gradient of u so that is a bug in tensor representation (probably a rounding issue).

I'm thinking this is an ill posed system and the rounding error in tensor representation in ffc happens to make it converge.

[Martin Sandve Alnæs]

matrix/vector is the same, ill posed test problem just happens to converge for tensor representation because of rounding error there.

[Prof Garth Wells]

Problem is missing boundary conditions, which is why it's ill-posed.

[Gabriel Balaban]

Missing BC and strange roundoff error sounds correct. Thanks for clearing that one up :-).