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.. _demo_nonmataching_interpolation:
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 :py:mod:`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 :math:`\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()
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