Demo 13 is not mathematically sound

[Matthias Liertzer]

In demo 13 the poisson equation is solved for pure Neumann boundary conditions in order to demonstrate mixed finite element spaces. However, the underlying problem is not well defined: For pure Neumann boundary conditions, f and g need to satisfy the compatibility condition \int_{\partial \Omega} g + \int_\Omega f = 0, which is not the case in the example (see http://eprints.ma.man.ac.uk/894/02/0-19-852868-X.pdf, page 1-2).

The example should be adapted to satisfy this condition, e.g. f=-4, g=1, and the condition should be mentioned in the help text.

Furthermore it would be interesting to see if it is possible for dolfin to detect such a case where the input is not well defined.

[Jan Blechta]

If you mean neumann-poisson demo

1. you're not correct - Lagrange multiplier takes care of the incompatibility

2. this is already reported as issue 117

[Matthias Liertzer]

Duplicate of #117.

[Matthias Liertzer]

thanks for pointing out that this issue has already been reported, however, the problem as it is stated is still ill-defined (in fact, the solution one obtains from fenics doesn't solve the Poisson equation). See my comment on the original bug report.