Specifying the source term in poissons equation from another solution

[dokken]

@mdbarrett

What I am not overly sure about is the form/type that f has.

f is a symbolic expression in your code (ufl expression). When you call dolfinx.fem.form or assemble_vector this is turned in to an evaluation of the symbolic expression at the quadrature points of your rhs integral and accumulated into the global vector, doing exactly what you set out to do.

@mdbarrett

Well I am at it - how do I get the array of points that goes with f?

You do not need the array to solve the problem. However if you would like to inspect f, you cal use dolfinx.fem.Expression:

f_compiled = dolfinx.fem.Expression(f, points_in reference_element)
Values = f_compiled.eval(mesh, np.arange(num_cells_local, dtype=np.int32))

As discussed in

dolfinx.fem.Expression - Function and expression evaluation — FEniCS Workshop

How to estimate the gradient along the vector between the two centers of adjacent cells?

Here is an example of how to get the midpoints, and the values of u at the midpoints: from mpi4py import MPI import dolfinx import numpy as np mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10) V = dolfinx.fem.functionspace(mesh, ("CG", 2)) u = dolfinx.fem.Function(V) u.interpolate(lambda x: x[0] + x[1] ** 2) Q = dolfinx.fem.functionspace(mesh, ("DG", 0, (mesh.geometry.dim,))) q = dolfinx.fem.Function(Q) q.interpolate(lambda x: x[: mesh.geometry.dim]) num_cells_local = ( mes…