Solution plot is showing piece wise linear functions even for higher order Lagrange elements

Question

Hi,

Below is a demo Poisson equation solver that was included in the Fenics installation. I have changed function space from CG_1 to CG_2. But the solution plot does not reflects this change. Plot is still showing a piecewise linear function.

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from dolfin import *
mesh = UnitSquareMesh(3,3)
V = FunctionSpace(mesh, "CG", 2)
def boundary(x):
return x[0] < DOLFIN_EPS or x[0] > 1.0 - DOLFIN_EPS

u0 = Constant(0.0)
bc = DirichletBC(V, u0, boundary)
u = TrialFunction(V)
v = TestFunction(V)
f = Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)")
g = Expression("sin(5*x[0])")
a = inner(grad(u), grad(v))*dx
L = f*v*dx + g*v*ds
u = Function(V)
solve(a == L, u, bc)
plot(u, interactive = True)

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Please tell me what am I missing. Thanks in advance.

Ajit

Answer 1

To my knowledge it's not supported. The bigger 'issue' for me is that it's also not supported by Paraview (or any other post-processor I know of/have access to). The workaround I have been going through is to interpolate the higher order solution onto a finer linear space.

If you need to write the solution on a finer mesh anyway, you could plot and write the finer mesh that's an interpolation of the higher order solution.

Comments

Yes, similar idea was suggested earlier by Oyvinev. Thanks.

Answer 2

I think it is just not supported, so projection to CG1 takes place before plotting. You could try Paraview.

Comments

I did try paraview. Still seeing piece wise linear plots only.

Answer 3

As Kristian says, this is not supported. Have a look here for ideas on how to improve the visualization.

Comments

OK. I will try that. Thanks