Thank you very much for looking at this.  Yes, the correct solution
is uniform at the same value as that on the boundary.  The reason the
solver tolerance values are so low, is that otherwise no solution can
be found, as the computer is trying to give a discontinuous solution
for a problem with continuous FE space.

This can't be right. If you set the tolerance to system_rhs.l2_norm() then even the zero vector is a sufficiently accurate solution. In any case, you are mixing discretization error (that's what you talk about when you consider approximating a discontinuous function with continuous finite elements) and iteration error (that's when you talk about solving a linear system Ax=b inexactly using an iterative solver). The two are independent, i.e., you can solve a linear system accurately even if the solution you get this way is a poor approximation of the continuous solution.

If you can't solve the linear system to high accuracy, then you need to find out why not. Just papering over it by setting the tolerance high is hiding the problem.

Best
 W.

------------------------------------------------------------------------
Wolfgang Bangerth               email:            [email protected]
                                www: http://www.math.tamu.edu/~bangerth/

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