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