Vector Poisson equation in a rectangle

\[\begin{split} \mathbb{S} \begin{cases} \Omega = [0, L_x] \times [0, L_y] \\ \textbf{f}(x,y)=(-y, x) \\ \textbf{u}_{\text{D}}(x,y=0)=(x, 1) \\ \textbf{u}_{\text{D}}(x,y=L_y)=(1, 2) \\ \textbf{u}_{\text{D}}(x=0,y)=(0, 0) \\ \textbf{u}_{\text{D}}(x=L_x,y)=(1, -1) \end{cases} \end{split}\]

from dolfinx.fem import FunctionSpace
from lucifex.mesh import rectangle_mesh, mesh_boundary
from lucifex.fem import Function, Constant
from lucifex.solver import bvp, BoundaryConditions
from lucifex.viz import plot_colormap, plot_line
from lucifex.utils import cross_section, get_component_fem_functions
from lucifex.pde.poisson import poisson


Lx = 2.0
Ly = 1.0
mesh = rectangle_mesh(Lx, Ly, 20, 10)
boundary = mesh_boundary(
    mesh, 
    {
        "left": lambda x: x[0],
        "right": lambda x: x[0] - Lx,
        "lower": lambda x: x[1],
        "upper": lambda x: x[1] - Ly,
    },
)
fs = FunctionSpace(mesh, ('P', 1, 2))
f = Function(fs, lambda x: (-x[1], x[0]), name='f')

bcs = BoundaryConditions(
    ('dirichlet', boundary['left'], (0.0, 0.0)),
    ('dirichlet', boundary['right'], Constant(mesh, (1.0, -1.0))),
    ('dirichlet', boundary['lower'], (lambda x: x[0], 1.0), 1),
    ('dirichlet', boundary['upper'], 1.0, 0),
    ('dirichlet', boundary['upper'], 2.0, 1),
)

u = Function(fs, name='u')
u_solver = bvp(poisson, bcs)(u, f)
u_solver.solve()

ux, uy = get_component_fem_functions(('P', 1), u, names=('ux', 'uy'))

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[1], line 22
     12 mesh = rectangle_mesh(Lx, Ly, 20, 10)
     13 boundary = mesh_boundary(
     14     mesh, 
     15     {
   (...)
     20     },
     21 )
---> 22 fs = FunctionSpace(mesh, ('P', 1, 2))
     23 f = Function(fs, lambda x: (-x[1], x[0]), name='f')
     25 bcs = BoundaryConditions(
     26     ('dirichlet', boundary['left'], (0.0, 0.0)),
     27     ('dirichlet', boundary['right'], Constant(mesh, (1.0, -1.0))),
   (...)
     30     ('dirichlet', boundary['upper'], 2.0, 1),
     31 )

File ~/miniconda3/envs/lucifex/lib/python3.10/site-packages/dolfinx/fem/function.py:481, in FunctionSpace.__init__(self, mesh, element, cppV, form_compiler_options, jit_options)
    479     super().__init__(mesh.ufl_domain(), element)
    480 else:
--> 481     e = ElementMetaData(*element)
    482     ufl_element = basix.ufl_wrapper.create_element(
    483         e.family, mesh.ufl_cell().cellname(), e.degree, gdim=mesh.ufl_cell().geometric_dimension())
    484     super().__init__(mesh.ufl_domain(), ufl_element)

TypeError: ElementMetaData.__new__() takes 3 positional arguments but 4 were given

x_axis, ux_x, y_value = cross_section(ux, 'y', 0.5)
plot_line((x_axis, ux_x), x_label='$x$', y_label=f'{u.name}_x(y={y_value:.2f})')

y_axis, ux_y, x_value = cross_section(ux, 'x', 0.5)
plot_line((y_axis, ux_y), x_label='$y$', y_label=f'{u.name}_x(x={y_value:.2f})')

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[2], line 1
----> 1 x_axis, ux_x, y_value = cross_section(ux, 'y', 0.5)
      2 plot_line((x_axis, ux_x), x_label='$x$', y_label=f'{u.name}_x(y={y_value:.2f})')
      4 y_axis, ux_y, x_value = cross_section(ux, 'x', 0.5)

NameError: name 'ux' is not defined

x_axis, uy_x, y_value = cross_section(uy, 'y', 0.5)
plot_line((x_axis, uy_x), x_label='$x$', y_label=f'{u.name}_y(y={y_value:.2f})')

y_axis, uy_y, x_value = cross_section(uy, 'x', 0.5)
plot_line((y_axis, uy_x), x_label='$y$', y_label=f'{u.name}_y(x={y_value:.2f})')

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[3], line 1
----> 1 x_axis, uy_x, y_value = cross_section(uy, 'y', 0.5)
      2 plot_line((x_axis, uy_x), x_label='$x$', y_label=f'{u.name}_y(y={y_value:.2f})')
      4 y_axis, uy_y, x_value = cross_section(uy, 'x', 0.5)

NameError: name 'uy' is not defined