Interpolation from a non-matching mesh

This example demonstrates how to interpolate functions between finite element spaces on non-matching meshes.

Note

Interpolation on non-matching meshes is not presently support in parallel. See https://bitbucket.org/fenics-project/dolfin/issues/162.

First, the modules dolfin and matplotlib are imported:

from dolfin import *
import matplotlib.pyplot as plt

Next, we create two different meshes. In this case we create unit square meshes with different size cells

mesh0 = UnitSquareMesh(16, 16)
mesh1 = UnitSquareMesh(64, 64)

On each mesh we create a finite element space. On the coarser mesh we use linear Lagrange elements, and on the finer mesh cubic Lagrange elements

P1 = FunctionSpace(mesh0, "Lagrange", 1)
P3 = FunctionSpace(mesh1, "Lagrange", 3)

We interpolate the function \(\sin(10x) \sin(10y)\)

v = Expression("sin(10.0*x[0])*sin(10.0*x[1])", degree=5)

into the P3 finite element space

# Create function on P3 and interpolate v
v3 = Function(P3)
v3.interpolate(v)

We now interpolate the function v3 into the P1 space

# Create function on P1 and interpolate v3
v1 = Function(P1)
v1.interpolate(v3)

The interpolated functions, v3 and v1 can ve visualised using the plot function

plt.figure()
plot(v3, title='v3')

plt.figure()
plot(v1, title='v1')

plt.show()