For a toy problem on a way to a more complicated system of PDEs, I tried to solve a variational problem of the form a(u,v) = \int (u \times v, u \times v) dx.
Edit: the above formulation is not well defined in the sense of FEM. What I rather meant was a(u,v) = \int (u \times g, u \times v) dx.
for some function g.
However I do end up with the Error, when I try to solve the variational problem with a non-linear solver,
UFLException: Index out of bounds.
which seems to happen in the UFL package.
My code is
from fenics import *
mesh = UnitSquareMesh(2, 2)
deg = 1
V=VectorFunctionSpace(mesh, "P",deg, dim=2)
u = Function(V)
v = TestFunction(V)
L = inner(cross(u, v) , cross(u, v) )*dx
solve(L==0, u)
I have to say I am quite overwhelmed with the error message because it does not really hint where I might have made a mistake. To me the variational problem seems well defined with a trivial solution, therefore the issue must occur during the assembly.
Would be very happy about every hint for my problem
Hi sorry, but I donβt think that you have a properly defined variational formulation. Either you should have a bilinear form a and a linear form L such as a(u, v)==L(v) for all v or a non-linear form F(u, v) == 0 for all v with F being non-linear with respect to the unknown function u but still being linear with respect to the test function v. Your a(u, v) makes no sense as it depends non-linearly on the test function vβ¦
Oh gosh, you are absolutely right. I made that rookie mistake when abstracting from my original problem.
Changed the code slightly, but I still run into the same Error.
Now it should (hopefully) really be well-definedβ¦
from fenics import *
mesh = UnitSquareMesh(2, 2)
deg = 1
V=VectorFunctionSpace(mesh, "P",deg, dim=2)
u = Function(V)
v = TestFunction(V)
g = interpolate(Expression(("sin(x[0])","1"),degree=2),V)
L = inner(cross(u, g) , cross(u, v) )*dx
solve(L==0, u)
The operator cross accepts as arguments two logically vector-valued expressions and returns a vector which is the cross product (vector product) of the two vectors:
