How to set a dirichlet boundary condition, which depends on a Function?

variational formulation
1

Hello,
I want to specify a Dirichlet boundary condition, which depends on a Function object rather than a constant (e.g. ScalarType(0), as is often the case in the standard examples I found). The following MWE produces a dtype error. My question is how this could be done properly.
Thank you.

import numpy
from ufl import (SpatialCoordinate, FiniteElement, MixedElement,
                 split, TestFunctions)
from dolfinx import fem, mesh
from dolfinx.fem import FunctionSpace, Function
from mpi4py import MPI
from petsc4py.PETSc import ScalarType


# Geometry and mesh
x_left  = -0.1
x_right = +0.1
NumberOfCells = int(1e3)

msh = mesh.create_interval(MPI.COMM_WORLD, NumberOfCells, points=(x_left, x_right))

x = SpatialCoordinate(msh)
CG1_elem = FiniteElement("CG", msh.ufl_cell(), 1)
ME_elem  = MixedElement([CG1_elem, CG1_elem])
ME = FunctionSpace(msh, ME_elem)

u_test, v_test = TestFunctions(ME)

w = Function(ME)

u, v = split(w)

# Left boundary
facet_l_bdry = mesh.locate_entities_boundary(msh, dim=0, marker=lambda x: numpy.isclose(x[0], x_left))
dof_l_bdry = fem.locate_dofs_topological(V=ME.sub(1), entity_dim=0, entities=facet_l_bdry)
f = 2*u
PoissonEq_dirichlet_bc_l = fem.dirichletbc(value=2*u, dofs=dof_l_bdry, V=ME.sub(1))
2

Interpolate 2*u into the suitable function space (for instance with dolfinx.fem.Expression) or simply by scaling all inputs of u by 2, i.e. u.x.array[:]*=2. and set is as shown in Test problem 2: Flow past a cylinder (DFG 2D-3 benchmark) — FEniCSx tutorial

u_inlet = Function(V)
inlet_velocity = InletVelocity(t)
u_inlet.interpolate(inlet_velocity)
bcu_inflow = dirichletbc(u_inlet, locate_dofs_topological(V, fdim, ft.find(inlet_marker)))
3

Hi dokken,
thank you for your answer. Maybe my MWE was too obscure (and also not really a MWE, sorry for that). My problem is that I am not able to provide any Function object in a Dirichlet boundary condition. I tried to further reduce the MWE:

import numpy as np
from ufl import SpatialCoordinate, FiniteElement
from dolfinx import fem, mesh
from dolfinx.fem import FunctionSpace, Function
from mpi4py import MPI

# Geometry and mesh
x_left = -0.1
x_right = +0.1
NumberOfCells = int(10)
msh = mesh.create_interval(MPI.COMM_WORLD, NumberOfCells, points=(x_left, x_right))
x = SpatialCoordinate(msh)
s_cg1 = FiniteElement("CG", msh.ufl_cell(), 1)
V = FunctionSpace(msh, s_cg1)

# left boundary
facet_l_bdry = mesh.locate_entities_boundary(msh, dim=0, marker=lambda x: np.isclose(x[0], x_left))
dof_l_bdry = fem.locate_dofs_topological(V=V, entity_dim=0, entities=facet_l_bdry)
u = Function(V)
PoissonEq_dirichlet_bc_l = fem.dirichletbc(value=u, dofs=dof_l_bdry, V=V)

which still throws a TypeError.