solving a pde on the surface of a solid

Question

I have an elliptic cylinder without caps.

And I am trying to solve for velocity field $u(\vec{x}, t)$ on its surface. This is a 3d vector field but the elements are triangles (2d). I think thats why it gives the error:

File "/usr/lib/python2.7/dist-packages/ufl/exproperators.py", line 407, in _getitem
ufl.log.UFLException: Fixed index out of range!
a = Indexed(self, indices)
a = Indexed(self, indices)
File "/usr/lib/python2.7/dist-packages/ufl/indexed.py", line 53, in __init__
File "/usr/lib/python2.7/dist-packages/ufl/indexed.py", line 53, in __init__
error("Fixed index out of range!")
File "/usr/lib/python2.7/dist-packages/ufl/log.py", line 154, in error
error("Fixed index out of range!")
File "/usr/lib/python2.7/dist-packages/ufl/log.py", line 154, in error
raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Fixed index out of range!
raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Fixed index out of range!

This surface has a simple geometry and hence we can use elliptic cylinder coordinates (u, v, z) with u constant and derive the weak formulation. And we have a rectangle in (v,z) and solve for this 2d velocity.

Is there some general way to deal with a similar curved surface geometry when the coordinate system transformation is not so obvious?

Comments

Please post a minimal code example along with the error message.

Answer 1

Marie Rognes had a presentation here that describes solving PDEs on a Moebius strip. I think that she does a much better job at explaining it than I could.