"Pointwise" BC

Question

Hi,

When I specify a displacement field to be a quadratic function, FEnICS will automatically insert new nodal points for quadratic interpolation.
Does anybody know that the boundary condition using "pointwise" will automatically constraint those new nodes?

Thanks,

Answer 1

Hi, the answer is yes. This can be seen in the source code and also tested easily

from dolfin import *

mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, 'CG', 2)

bdry = CompiledSubDomain('near(x[0], 0)')
value = Expression('x[1]*(1-x[1])', degree=2)
bc = DirichletBC(V, value, bdry, method='pointwise')

# Set quadratic f to quad function
f = Function(V)
f.vector().zero()
bc.apply(f.vector())

# There should be zero error between f and prescribed value on the boundary
facet_f = FacetFunction('size_t', mesh, 0)
bdry.mark(facet_f, 1)
e = (f-value)**2*ds(domain=mesh, subdomain_data=facet_f, subdomain_id=1)

print assemble(e)
plot(f, interactive=True)