Hi everyone,

currently I am trying to compute a vector valued Poisson problem in cylindrical coordinates, under the assumption of rotational symmetry which allows the problem to be reduced into a 2-dimensional one. The weak formulation of this is the following:

[tex]

\int_{\Omega^{2d}} x \nabla u : \nabla v + \frac{1}{x} u_x v_x dx dy

[/tex]

- The term 1/x * u_x * v_x term is of course singular on the rotational axis (r → x= 0). However I have u_x = 0 on the boundary x = 0 so I do not have to solve on this boundary.
- In order to not evaluate anything on the boundary, I have manually changed the integration rule to only use interior points.

However, the stiffness-matrix still contains ‘nan’ values for the dofs (see attached MWE).

https://ngsolve.org/media/kunena/attachments/830/Poission_CylCoord_RotSym.py

Can anyone explain/solve this problem?

Best wishes,

Henry

Attachment: Poission_CylCoord_RotSym.py