Small question about writing dot product in UFL

variational formulation
2

What is u ? If it’s a vector function, then grad(u) would be a second order tensor and so would dot(as_matrix(a), grad(u)). On the other hand dot(u, c) would be a scalar. Also you need not use numpy arrays, you can directly pass lists to as_matrix and as_vector, namely

a = as_matrix([[0.5*A_3**2*x[2]**2,0,0.5*A_3**2*x[0]*x[2]],
[0,0.5*(A_1**2+A_2**2+A_3**2*(x[2]/x[0])**2),0],
[0.5*A_3**2*x[0]*x[2],0,0.5*A_3**2*x[0]**2]])

c = as_vector([-0.5*A_3**2*x[0]+(A_3**2/2-A_4)*x[0],
-A_5,
-0.5*A_3**2*x[2]+(A_3**2/2+A_4)*x[2]])

If u is a scalar function (from your previous post) then you don’t need a dot product between c and u, it’s simply c*u

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