# Stokes problem in 3D -DOLFINx

**URL:** <https://fenicsproject.discourse.group/t/stokes-problem-in-3d-dolfinx/15322>\
**Category:** General\
**Created:** [July 23, 2024, 7:28am UTC](https://fenicsproject.discourse.group/t/stokes-problem-in-3d-dolfinx/15322 "2024-07-23T07:28:48Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![steven\_sanchez](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/steven_sanchez/32/7321_2.png) [@steven\_sanchez](https://fenicsproject.discourse.group/u/steven_sanchez)\
**Post date:** [July 23, 2024, 7:28am UTC](https://fenicsproject.discourse.group/t/stokes-problem-in-3d-dolfinx/15322/1 "2024-07-23T07:28:48Z")

</div>

Good day to the community, I have a problem reproducing the code of [[1](https://fenicsproject.discourse.group/t/steady-stokes-equation-3d-dolfinx/9709/4)]. I have already updated the code to DOLFINX version 0.8.0 but I get the following error:

```auto
Traceback (most recent call last):
  File "/home/oscar/viskex/nuevo1.py", line 79, in <module>
    A = fem.petsc.assemble_matrix(a, bcs=bcs)
  File "/usr/lib/python3.10/functools.py", line 889, in wrapper
    return dispatch(args[0]. __class__ )(*args, **kw)
  File "/usr/lib/petsc/lib/python3/dist-packages/dolfinx/fem/petsc.py", line 424, in assemble_matrix
    A = _cpp.fem.petsc.create_matrix(a._cpp_object)
AttributeError: 'list' object has no attribute '_cpp_object'

```

I attach the code that I have updated:

```auto
import numpy as np
import dolfinx 

import ufl
from basix.ufl import element, mixed_element
from petsc4py import PETSc
from mpi4py import MPI
from dolfinx import fem
from dolfinx.fem import form
from dolfinx.fem.petsc import assemble_matrix_block, assemble_vector_block
from ufl import div, grad, inner

N = 16
mesh = dolfinx.mesh.create_unit_cube(MPI.COMM_WORLD, N, N, N,
                                     cell_type=dolfinx.mesh.CellType.hexahedron)
P2 = element("Lagrange", mesh.basix_cell(), 2, shape=(mesh.geometry.dim,))
P1 = element("Lagrange", mesh.basix_cell(), 1)
TH = mixed_element([P2, P1])
W = dolfinx.fem.functionspace(mesh, TH)

def right(x, tol=1e-14): return x[0] > 1 - tol

def top_bottom(x, tol=1e-14):
    return np.logical_or(
        np.isclose(x[1], 0, atol=tol), np.isclose(x[1], 1, atol=tol))

V, V_to_W = W.sub(0).collapse()

# No-slip boundary condition for velocity
nonslip = dolfinx.fem.Function(V)
nonslip.x.array[:]=1
nonslip_facets = dolfinx.mesh.locate_entities_boundary(
    mesh, mesh.topology.dim-1, top_bottom)
nonslip_dofs = dolfinx.fem.locate_dofs_topological(
    (W.sub(0), V), mesh.topology.dim-1, nonslip_facets)
bc0 = dolfinx.fem.dirichletbc(nonslip, nonslip_dofs, W.sub(0))

# Inflow boundary condition for velocity

def inflow(x):
    zero_comp = np.zeros(x.shape[1], dtype=np.float64)
    return (-np.sin(np.pi*x[1]), zero_comp, zero_comp)

inflow_facets = dolfinx.mesh.locate_entities_boundary(mesh, mesh.topology.dim-1,
                                                      right)
inflow_dofs = dolfinx.fem.locate_dofs_topological((W.sub(0), V), mesh.topology.dim-1,
                                                  inflow_facets)
u_bc = dolfinx.fem.Function(V)
u_bc.interpolate(inflow)
bc1 = dolfinx.fem.dirichletbc(u_bc, inflow_dofs, W.sub(0))

bcs = [bc0, bc1]

(u, p) = ufl.TrialFunctions(W)
(v, q) = ufl.TestFunctions(W)
f = dolfinx.fem.Constant(mesh, (0., 0., 0.))

dx = ufl.Measure("dx", domain=mesh)
# a = ufl.inner(ufl.grad(u), ufl.grad(v)) * dx + \
    # ufl.div(v)*p*dx + q*ufl.div(u)*dx
# L = ufl.inner(f, v) * dx

a = form([[inner(grad(u), grad(v)) * dx, inner(p, div(v)) * dx], [inner(div(u), q) * dx, None]])
L = form([inner(f, v) * dx, inner(dolfinx.fem.Constant(mesh, PETSc.ScalarType(0)), q) * dx]) # type: ignore

A = fem.petsc.assemble_matrix(a, bcs=bcs)
A.assemble()
b = dolfinx.fem.petsc.assemble_vector(L)
dolfinx.fem.petsc.apply_lifting(b, [a], [bcs])
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc(b, bcs)
b.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)

# Preconditioner matrix form
Pf = dolfinx.fem.form(ufl.inner(ufl.grad(u), ufl.grad(v)) * dx + p * q * dx)
P = dolfinx.fem.petsc.assemble_matrix(Pf, bcs=bcs)
P.assemble()

ksp = PETSc.KSP().create(mesh.comm)
ksp.setOperators(A, P)
ksp.setType(PETSc.KSP.Type.MINRES)
pc = ksp.getPC()
pc.setType("hypre")
pc.setHYPREType("boomeramg")
pc.setUp()

# To view Preconditioner info
# pc.view()

wh = dolfinx.fem.Function(W)
ksp.solve(b, wh.vector)

# To view solver info
# ksp.view()

uh = wh.sub(0).collapse()
p = wh.sub(1).collapse()

print(f"Converged Reason {ksp.getConvergedReason()}" +
      f"\nNumber of iterations {ksp.getIterationNumber()}")

with dolfinx.io.VTXWriter(mesh.comm, "u.bp", [uh]) as vtx:
    vtx.write(0.)

with dolfinx.io.VTXWriter(mesh.comm, "p.bp", [uh]) as vtx:
    vtx.write(0.)

```

Thank you in advance for your help.

---

<div class="post-metadata">

**Author:** ![francesco-ballarin](https://avatars.discourse-cdn.com/v4/letter/f/f05b48/32.png) [@francesco-ballarin](https://fenicsproject.discourse.group/u/francesco-ballarin)\
**Post date:** [July 23, 2024, 9:53am UTC](https://fenicsproject.discourse.group/t/stokes-problem-in-3d-dolfinx/15322/2 "2024-07-23T09:53:51Z")

</div>

You seem to be mixing up two different codes.  
You are using a `mixed_element`, hence your forms shouldn’t be block forms.  
If you are willing to use block forms, then define the two spaces for velocity and pressure separately, and use block assembly from `dolfinx.fem.petsc` (e.g., `assemble_matrix_block`.