.. _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()