Visualise basis functions

I/O
1

Hello all

I am trying to visualise the basis functions used in different choices of elements. So far I am successfull producing plots of them when the element degree is 1 as follows.

from dolfinx import fem, mesh
from mpi4py import MPI
import matplotlib.pyplot as plt
domain = mesh.create_unit_interval(MPI.COMM_SELF, 4)
V = fem.FunctionSpace(domain, ('CG',1))
v = fem.Function(V)
v.x.array[4] = 1
plt.plot(v.x.array)

Here the 4 in v.x;array[4] is a chosen index between the values of the local range (V.dofmap.index_map.local_range).

For 2D meshes I do the visualisation with pyvista.

For this example (with Lagrange elements of degree 1), I artificially set the value of the function at a node to 1. I was wondering if there is some quicker/more elegant way to do this and if there is something possible for higher order degree elements, e.g. Lagrange elements with degree 2 ((ā€˜CGā€™, 2) in the functionspace) or higher.

I am happy with any advice and/or pointers on how to do this.

Many thanks in advance!

2

I would suggest you have a look at defelement: DefElement
as it has figures of the basis functions for a large variety of elements.

The figures are generated with @mscroggs SymFem: GitHub - mscroggs/symfem: A symbolic finite element definition library. I guess he can point you to how you can make arbitrary plots

1 Like
3

Thank you dokken, the links you provided look interesting!