How convert a vector to UFL vector function to pass in errornorm function

variational formulation
1

Hi FEniCS Community,

I am solving a mixed problem for nonlinear elasticity, I have defined my exact solution as bellow:

Ke_1 = as_vector((sin(2*x[0]/R)pow(sin(x[1]/R),2) , sin(2x[1]/R)*pow(sin(x[0]/R),2) , 0.0)) # the first row of displacement gradient

Ke_2 = as_vector(( 0.0, sin(2*x[1]/R)pow(sin(x[2]/R),2), sin(2x[2]/R)*pow(sin(x[1]/R),2))) # the second row of displacement gradient

Ke_3 = as_vector((sin(2*x[0]/R)pow(sin(x[2]/R),2), 0.0, sin(2x[2]/R)*pow(sin(x[0]/R),2))) # 3rd row of displacement gradient

def_grad = as_tensor([[1.0 + Ke_1[0], Ke_1[1], Ke_1[2]], [Ke_2[0], 1.0 + Ke_2[1], Ke_2[2]], [Ke_3[0], Ke_3[1], 1.0 + Ke_3[2]]]) # deformation gradient

Stress_ES = mudef_grad + (2lamln(det(def_grad.Tdef_grad)) - mu)*inv(def_grad.T) #stress tensor
Pe_1 = Stress_ES[0,:] # Extract 1st row of stress
Pe_2 = Stress_ES[1,:] # Extract 2nd row of stress
Pe_3 = Stress_ES[2,:] # Extract 3st row of stress

Pe_1, Pe_2 and Pe_3 are three rows of my stress tensor. (“stress” belongs to “BDM” and ““displacement”” belongs to ““N2curl””.

After computing my approximate solution regarding stress, I am going to pass both exact solutions and approximate solutions to “errornorm” function to obtain my error. But Pe_1, Pe_2, Pe_3 are not UFL functions, so I interpolate them to specific Function Space but I am getting this error:

TypeError: in method ‘Function_interpolate’, argument 2 of type ‘dolfin::GenericFunction const &’
Aborted (core dumped)

So I have two questions:

  1. Is there a way that I can define Pe_1, Pe_2, Pe_3 as Expression?
  2. How should fix the error I am getting?

Thank you in advance.

2

If you only want to compute the norms of the error, you could define them manually instead of using errornorm, e.g. for the L^2 norm:

norm_L2 = sqrt( assemble( ( exact_solution - numerical_solution )**2 * dx ) )
3

@volkerk’s solution is a valid solution. However, if you really want to interpolate into a higher function space to avoid floating point errors, you can use that Expression supports tensors, for instance consider this 2D example:

from dolfin import *
expr = Expression((("x[0]","x[1]"),("x[0]*x[1]","x[0]")), degree=3)  
print(expr.ufl_shape)

yields:
(2, 2).