Second-order Serendipity Elements [dirichletbc]

Errors
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1

Hi,

I’m conducting a benchmark to compare my code with commercial FEM software, which typically only offer Serendipity elements for plane stress cases, rather than Lagrange Elements.

I followed the suggestion from @dokken on dealing with Serendipity Elements as discussed in this FEniCS Project forum thread. However, I encountered an issue when trying to create a Dirichlet boundary condition in just one direction, resulting in the following error:
RuntimeError: Constant can be used only with point-evaluation elements

I’m trying to fix a displacement of 0 in the x-direction at the bottom of the domain. Here’s a code snippet illustrating my problem:

import dolfinx
from mpi4py import MPI
import numpy as np
from petsc4py.PETSc import ScalarType

def boundary_bottom(x: List[float]) -> bool:
    return np.isclose(x[1], min(x[1]))

domain = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 1, 1, dolfinx.mesh.CellType.quadrilateral)
v_func_space = dolfinx.fem.VectorFunctionSpace(domain, ("S", 2))
        
sub_0, _ = v_func_space.sub(0).collapse()
edges = dolfinx.mesh.locate_entities_boundary(domain, domain.topology.dim - 1, boundary_bottom)
boundary_dofs = dolfinx.fem.locate_dofs_topological((v_func_space.sub(0), sub_0), domain.topology.dim - 1, edges)

bc = dolfinx.fem.dirichletbc(ScalarType(0), boundary_dofs[0], v_func_space.sub(0))

What doesn’t make sense is that this approach works for second-order Lagrange elements, as well as for first-order Serendipity and Lagrange Elements.

Thanks in advance for any help!

2

Simplest workaround I can think of is to replace your final line with

# bc = dolfinx.fem.dirichletbc(ScalarType(0), boundary_dofs[0], v_func_space.sub(0))
zero_scalar = dolfinx.fem.Function(sub_0)
bc = dolfinx.fem.dirichletbc(zero_scalar, boundary_dofs, v_func_space.sub(0))
1 Like
3

Thanks, @francesco-ballarin!
Could you also tell me how the code would change if the displacement values are a constant instead of zero?

Additionally, out of curiosity, do you know why my solution doesn’t work with Serendipity Elements but works with Lagrange Elements?

4

Could you also tell me how the code would change if the displacement values are a constant instead of zero?

Just interpolate the value into a dolfinx.fem.Function

Additionally, out of curiosity, do you know why my solution doesn’t work with Serendipity Elements but works with Lagrange Elements?

I can’t claim to know much about Serendipity Elements, because I’ve never used them. Still, the error

RuntimeError: Constant can be used only with point-evaluation elements

aligns with what I can see from DefElement, i.e. that DOFs 4 to 7 in S elements are given by the average on edges.

If you look at the similar page for Q elements at DefElement
you will see that DOFs 4 to 7 are again associated to edges, but are pointwise evaluation at the midpoint, rather than an integral.

1 Like
5

I followed your suggestion to interpolate the value into a dolfinx.fem.Function and it worked perfectly!

Your explanation was excellent and now the error makes complete sense.

Thanks, Francesco, for your help!