# Mixed Poisson problem

**URL:** <https://fenicsproject.discourse.group/t/mixed-poisson-problem/17351>\
**Category:** General\
**Created:** [April 1, 2025, 3:05pm UTC](https://fenicsproject.discourse.group/t/mixed-poisson-problem/17351 "2025-04-01T15:05:06Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Neofytos\_Neofytou](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/neofytos_neofytou/32/7934_2.png) [@Neofytos\_Neofytou](https://fenicsproject.discourse.group/u/Neofytos_Neofytou)\
**Post date:** [April 1, 2025, 3:05pm UTC](https://fenicsproject.discourse.group/t/mixed-poisson-problem/17351/1 "2025-04-01T15:05:06Z")

</div>

Hello everyone,

I am using FEniCSX (fenics-dolfinx 0.9.0) with Linux (Ubuntu 24.04.2 LTS) which i installed with apt.

I create a custom made mesh using the code i found there [Mesh generation](https://jsdokken.com/FEniCS23-tutorial/src/mesh_generation.html)

Now i modify the code from [Mixed formulation for the Poisson equation](https://docs.fenicsproject.org/dolfinx/v0.7.2/python/demos/demo_mixed-poisson.html).

```auto
from mpi4py import MPI
from petsc4py import PETSc
import numpy as np
from basix.ufl import element, mixed_element
from dolfinx import fem, io, mesh
from dolfinx.fem.petsc import LinearProblem
from ufl import (Measure, SpatialCoordinate, TestFunctions, TrialFunctions,
div, exp, inner)
import matplotlib.pyplot as plt
import pyvista
import basix.ufl
import dolfinx
import ufl

#domain = mesh.create_unit_square(MPI.COMM_WORLD, 32, 32, mesh.CellType.quadrilateral)

nodes = np.array([[1.0, 0.0], [2.0, 0.0], [3.0, 2.0], [1, 3]], dtype=np.float64)
connectivity = np.array([[0, 1, 2], [0, 2, 3]], dtype=np.int64)
c_el = ufl.Mesh(basix.ufl.element("CG", "triangle", 1, shape=(nodes.shape[1],)))
domain = dolfinx.mesh.create_mesh(MPI.COMM_SELF, connectivity, nodes, c_el)

k = 4
Q_el = element("BDM", domain.basix_cell(), k)
P_el = element("CG", domain.basix_cell(), k - 1)
V_el = mixed_element([Q_el, P_el])
V = fem.functionspace(domain, V_el)

(sigma, u) = TrialFunctions(V)
(tau, v) = TestFunctions(V)

x = SpatialCoordinate(domain)
f = 10.0 * exp(-((x[0] - 0.5) * (x[0] - 0.5) + (x[1] - 0.5) * (x[1] - 0.5)) / 0.02)

dx = Measure("dx", domain)
a = inner(sigma, tau) * dx + inner(u, div(tau)) * dx + inner(div(sigma), v) * dx
L = -inner(f, v) * dx

fdim = domain.topology.dim - 1
facets_top = mesh.locate_entities_boundary(domain, fdim, lambda x: np.isclose(x[1], 1.0))
Q, _ = V.sub(0).collapse()
dofs_top = fem.locate_dofs_topological((V.sub(0), Q), fdim, facets_top)

def f1(x):
values = np.zeros((2, x.shape[1]))
values[1, :] = np.sin(5 * x[0])
return values

f_h1 = fem.Function(Q)
f_h1.interpolate(f1)
bc_top = fem.dirichletbc(f_h1, dofs_top, V.sub(0))

facets_bottom = mesh.locate_entities_boundary(domain, fdim, lambda x: np.isclose(x[1], 0.0))
dofs_bottom = fem.locate_dofs_topological((V.sub(0), Q), fdim, facets_bottom)

def f2(x):
values = np.zeros((2, x.shape[1]))
values[1, :] = -np.sin(5 * x[0])
return values

f_h2 = fem.Function(Q)
f_h2.interpolate(f2)
bc_bottom = fem.dirichletbc(f_h2, dofs_bottom, V.sub(0))

bcs = [bc_top, bc_bottom]

problem = LinearProblem(a, L, bcs=bcs, petsc_options={"ksp_type": "preonly", "pc_type": "lu",
"pc_factor_mat_solver_type": "mumps"})
try:
w_h = problem.solve()
except PETSc.Error as e: # type: ignore
if e.ierr == 92:
print("The required PETSc solver/preconditioner is not available. Exiting.")
print(e)
exit(0)
else:
raise e

sigma_h, u_h = w_h.split()

with io.XDMFFile(domain.comm, "out_mixed_poisson/u.xdmf", "w") as file:
file.write_mesh(domain)
file.write_function(u_h)

```

For k=1 is working but once i increase the value of k i get the following error

```auto
Traceback (most recent call last):
  File "/home/vboxuser/Desktop/demo_mixed-poisson.py", line 82, in <module>
    file.write_function(u_h)
  File "/usr/lib/petsc/lib/python3/dist-packages/dolfinx/io/utils.py", line 252, in write_function
    super().write_function(getattr(u, "_cpp_object", u), t, mesh_xpath)
RuntimeError: Degree of output Function must be same as mesh degree. Maybe the Function needs to be interpolated?

```

Even when i interpolate the solution into a Function space with the code

```auto
V_out = fem.functionspace(domain, element("CG", domain.basix_cell(), k))
u_h_interp = fem.Function(V_out)
u_h_interp.interpolate(u_h)

```

i get the same

```auto
Traceback (most recent call last):
  File "/home/vboxuser/Desktop/demo_mixed-poisson.py", line 86, in <module>
    file.write_function(u_h_interp)
  File "/usr/lib/petsc/lib/python3/dist-packages/dolfinx/io/utils.py", line 252, in write_function
    super().write_function(getattr(u, "_cpp_object", u), t, mesh_xpath)
RuntimeError: Degree of output Function must be same as mesh degree. Maybe the Function needs to be interpolated?

```

How can this be corrected?

---

<div class="post-metadata">

**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [April 1, 2025, 4:33pm UTC](https://fenicsproject.discourse.group/t/mixed-poisson-problem/17351/2 "2025-04-01T16:33:18Z")

</div>

Use another writer than xdmf, as suggested in: [How to make Von Mises Stress look better - #10 by dokken](https://fenicsproject.discourse.group/t/how-to-make-von-mises-stress-look-better/17013/10)

Please search for the error message on the forum before posting  
[https://fenicsproject.discourse.group/search?context=topic&context\_id=17351&q=RuntimeError%3A%20Degree%20of%20output%20Function%20must%20be%20same%20as%20mesh%20degree.%20Maybe%20the%20Function%20needs%20to%20be%20interpolated%3F%20order%3Alatest&skip\_context=true](https://fenicsproject.discourse.group/search?context=topic&context_id=17351&q=RuntimeError%3A%20Degree%20of%20output%20Function%20must%20be%20same%20as%20mesh%20degree.%20Maybe%20the%20Function%20needs%20to%20be%20interpolated%3F%20order%3Alatest&skip_context=true)  
as there are many posts on the same topic.