Double derivative of Shape Function

Question

Hi, I am novice user of Fenics.
How can I calculate and visualize double derivate of the shape function ?

d2N/dx2

my problem is simple but i am not getting any idea, small help save my time.

Thanks

Answer 1

I think that this question may help you
https://fenicsproject.org/qa/2878/visualising-shape-functions

Sample code adapted from the accepted answer

from dolfin import *
mesh = UnitSquareMesh(10,10)
plot(mesh)

V = FunctionSpace(mesh, 'CG', 2)
v = Function(V)
v.vector()[51] = 1

mesh2 = UnitSquareMesh(100,100)
V2 = FunctionSpace(mesh2, 'CG', 2)
v2 = project(v.dx(0).dx(0), V2)
plot(v2)
interactive()

Comments

Thanks, I seems working

Answer 2

Elements in FEniCS are only piecewise continuous. This means that
the derivatives are discontinuous and the second order derivatives are
delta function at element boundaries. Hence, second order derivatives should
be use with care. In usual FEM methods the second order derivative is defined
only weakly.