Save only nodal values for quadratic Lagrange elements (p2)

Question

Hello,

Is there a way to save the solution only at nodal values (vertices of triangular elements) instead than at all degrees of freedom? I would like to do that for Lagrange quadratic elements.

Now, after computing the solution a1, I do the following:

X=V.tabulate_dof_coordinates()
X.resize((V.dim(), 2))
x = X[:,0]
y = X[:,1]
a_values  = a1.vector().array()
np.savetxt("results/a_p2.csv", np.c_[x, y, a_values], delimiter=",")

Is there a way to save only nodal values?

Answer 1

Also you can do something like this:

from dolfin import *

mesh = UnitSquareMesh(5,5)
V = FunctionSpace(mesh, "CG", 2)

# Extract dofs at mesh vertices
dofmap = V.dofmap()
dofs = dofmap.dofs(mesh, 0)

# Test
u = interpolate(Expression("x[0]*x[1]"), V)   # Create P2 function
print u.vector()[dofs]                        # Print only dofs at vertices

Comments

Hey, that's pretty nice!

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Thank you hernan_mella!

Answer 2

Interpolate the P2 function onto the P1 FunctionSpace, and save the resulting NumPy array.

from fenics import *

mesh = UnitSquareMesh(2,2)
P1   = FunctionSpace(mesh, 'CG', 1)
P2   = FunctionSpace(mesh, 'CG', 2)

x = Function(P2)

y = interpolate(x, P1)

y_a = y.vector().array()

Comments

You probably wanted to interpolate to P1, ;)

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Thank you!!! Easy solution :)