Define Nonlinear problem with ufl.derivative and MixedElement

variational formulation
1

Hello,

I would like to solve a nonlinear problem using ufl.derivative and MixedElement. Here is a (much simplified) example code of what I am trying to solve:

import dolfinx
import ufl
import numpy as np
from mpi4py import MPI
import dolfinx.fem.petsc
from dolfinx import nls, fem, io, mesh


L = 0.125  # total length
delta = 2.0  # aspect ratio
d=L *delta  # thickness

my_domain = dolfinx.mesh.create_rectangle(MPI.COMM_WORLD, [np.array([0, 0]), np.array([L, d])], [10,10], cell_type=dolfinx.mesh.CellType.quadrilateral)

u_el = ufl.VectorElement('Lagrange', my_domain.ufl_cell(), degree=1, dim=2)
phi_el = ufl.FiniteElement('Lagrange', my_domain.ufl_cell(), degree=1)
mixed_el = ufl.MixedElement([u_el, phi_el]) # mixed element
V = dolfinx.fem.FunctionSpace(my_domain, mixed_el) 

u_gen = fem.Function(V)
u, phi = ufl.split(u_gen)
v = ufl.TrialFunction(V)

dim = len(u)
I = ufl.variable(ufl.Identity(dim))
F = ufl.variable(I + ufl.grad(u))
C = ufl.variable(F.T * F)
E = ufl.variable(1/2*(C-I))

dx = ufl.Measure("dx", domain=my_domain)
potential_energy = (ufl.tr(E)**2+ufl.inner(phi,phi))*dx

residual = ufl.derivative(potential_energy, u_gen, v)
problem = dolfinx.fem.petsc.NonlinearProblem(residual, u_gen, bcs=[])

I get the following error message:

ValueError: too many values to unpack (expected 2)

I am not sure what is the correct syntax to define such a nonlinear problem.
Many thanks in advance for your help!

Claire

2

Hi Claire,
v should be a TestFunction rather than a TrialFunction

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