How to evaluate basis function at points of cell

Question

How to evaluate basis functions of a space on a list of points at cells?

Answer 1

Hi, consider adapting

from dolfin import *
import numpy as np

mesh = UnitSquareMesh(3, 3)
V = FunctionSpace(mesh, 'CG', 3)
f = interpolate(Expression('3*x[0]*x[0]*x[1]-2*x[1]*x[1]*x[0]'), V)
el = V.element()

# Where to evaluate
x = np.array([0.33, 0.55])

# Find the cell with point
x_point = Point(*x) 
cell_id = mesh.bounding_box_tree().compute_first_entity_collision(x_point)
cell = Cell(mesh, cell_id)
coordinate_dofs = cell.get_vertex_coordinates()

# Array for values. Here it is simply a single scalar
values = np.zeros(1, dtype=float)
for i in range(el.space_dimension()): 
    el.evaluate_basis(i, values, x, coordinate_dofs, cell.orientation()) 
    print i, values

You can also evaluate all basis functions of the cell at once by evaluate_basis_all.

Comments

Can you explain the ordering of the basis function evaluations? That is, what node dof index is associated with each value of i?