Dear firedrake users, I try to solve a variational inequality using snes-firedrake.

I have two unknown functions say (theta,w)

so the functionspace is Vh = MixedFunctionSpace([Th,Wh]) 

 where

Th = FunctionSpace(mesh, "Lagrange", 1)
Wh = FunctionSpace(mesh, "Lagrange", 2)

the inequality constraint concerns only $w$

I set : 

obstacle = Function(Vh.sub(1)).interpolate((Constant(-0.03)))

upper = Function(Vh.sub(1)).interpolate(Constant(1e10))

solver.solve(bounds=(obstacle, upper)) 

but this line causes the following error:

File "/Users/maths/Desktop/Firedrake/VI/Timoshenko-obs.py", line 64, in <module>
    solver.solve(bounds=(obstacle, upper))
  File "petsc4py/PETSc/Log.pyx", line 188, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 189, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/Users/maths/firedrake/src/firedrake/firedrake/adjoint_utils/variational_solver.py", line 89, in wrapper
    out = solve(self, **kwargs)
  File "/Users/maths/firedrake/src/firedrake/firedrake/variational_solver.py", line 312, in solve
    self.snes.setVariableBounds(lb, ub)
  File "petsc4py/PETSc/SNES.pyx", line 1978, in petsc4py.PETSc.SNES.setVariableBounds
petsc4py.PETSc.Error: error code 75
[0] SNESVISetVariableBounds() at /Users/maths/firedrake/src/petsc/src/snes/impls/vi/vi.c:424
[0] SNESVISetVariableBounds_VI() at /Users/maths/firedrake/src/petsc/src/snes/impls/vi/vi.c:443
[0] Arguments are incompatible

[0] Incompatible vector lengths lower bound = 201 solution vector = 302 

Hope that one can help me ...

Best regards.

Smail. 

On Fri, Apr 11, 2025 at 9:11 AM Smail Merabet <merabetsmail@gmail.com> wrote:

Dear firedrake users, 

I try to solve a fourth-order 1d nonlinear problem using the Hermite element in firedrake.

The functional space for the weak solution is:

$$\mathcal{H}\times \mathcal{H}/times H^{2}_{0} $$ 

where,

$$
\mathcal{H} = \left\lbrace f\in H^2([0,\ell]), \; f(0)=0, \; f'(0)=0 \right\rbrace.
$$ 

I can't impose the boundary conditions correctly. When I compile the code, I get the following error: 

 FiniteElement('Hermite', interval, 3), name=None, index=1, component=None), IndexedProxyFunctionSpace(<firedrake.mesh.MeshTopology object at 0x125a2ce80>, FiniteElement('Hermite', interval, 3), name=None, index=2, component=None), name='None_None_None'), Mesh(VectorElement(FiniteElement('Lagrange', interval, 1), dim=1), 0)), 9) defined on incompatible FunctionSpace!

Note the same problem was implemented using FEniCS with C0-interior penalty method, in the reference (sec. 3 eq 3.12-3.13): 

Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability
by:
Matteo Brunetti , Antonino Favata  and Stefano Vidoli.

I attached the codes to this email.

Thanks in advance

Smail MERABET

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