Accessing the basis function of a Finite Element

[chenyongxin]

You need to find the reference coordinate first by using pull_back function. See the following for the basis function evaluation process:

Evaluate_basis_all in dolfinx

The DOLFINx way to do this would be to: Figure out which cell the point x is in (using dolfinx.compute_colliding_cells, as done in: Implementation — FEniCSx tutorial) Pull these coordinates back to the reference element, using mesh.geometry.cmap.pull_back (dolfinx/fem.cpp at 48ece0087588f5f274a36aec223abb129fa59e8e · FEniCS/dolfinx · GitHub) Use basix.FiniteElement(element_of choice).tabulate(1, X_ref) to tabulate at the reference points. An example of the last step can be found in: asimov-cu…

and the practical implmentation:

Evaluate_basis_all in dolfinx

I think you can achieve what you want with the following: from mpi4py import MPI import dolfinx import ufl import numpy as np domain = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 1, 1) tdim = domain.topology.dim V = dolfinx.fem.FunctionSpace(domain, ("CG", 2)) point = np.array([[0.2, 0.3, 0]]) bb = dolfinx.geometry.BoundingBoxTree(domain, tdim) bbox_collisions = dolfinx.geometry.compute_collisions(bb, point) cells = dolfinx.geometry.compute_colliding_cells(domain, bbox_collisions, point) c…

Note it is subject to change depending on the version of DOLFINx you use.