Problem with creating vector element

dolfinx
1

Hello everyone,

I’m new to FEniCSx and have been learning by solving some scalar-valued PDEs, which I managed to do successfully using the provided documentation. However, I’m currently facing issues when working with vector PDEs,
specifically in creating 3D vector elements.Below is the code snippet

domain = mesh.create_interval(MPI.COMM_WORLD, num_elements, [0, L])
typeelement = element("Lagrange", domain.basix_cell(), 1,shape = (3,) ,dtype=default_real_type)
V = fem.functionspace(domain, typeelement)

# Define trial and test functions
r = fem.Function(V)  # Solution function (trial function)
r_prime = ufl.grad(r) 
norm_r_prime = ufl.sqrt(ufl.dot(r_prime, r_prime))

when i run the above code,the error is shown as following.

norm_r_prime = ufl.sqrt(ufl.dot(r_prime, r_prime))
return Dot(a, b)
raise ValueError("Dimension mismatch in dot product.")

can you please help me with resolving this issue and it.

2

Here you probably want to use ufl.inner

3

Thank you it worked.But i got another two problems:
first,
the shape of r_prime is (3,1,1). whereas ‘r’ and testfunction ’ w’ is of (3,1),.which is same as defined.The problem is that i am not able to do ufl.inner(w,r_prime) because of shape difference.Can please help me to convert r_prime to 3x1 vector.

and second question is unrelated to this, which is defining constant (3x1) vector.
example snippet is

gr= np.transpose([0,-9.81,0])
`g= fem.Constant(domain, gr)`

the shape is of showing as (3,), how to make g 3x1 vector.

4

You could simply go the other way, and make r_prime a (3, ) vector:

r_prime = ufl.grad(r)[:, 0]

or simply just differentiate with respect to x direction

r_prime = r.dx(0)
5

Thank you for the help it worked