Clarified implementation of breaction

[fafroo]

Let us assume a charge density $Q$ confined to a surface (surface charge density) between domains $\Omega-$ and $\Omega+$. The surface charge density causes a discontinuity of the normal components of the displacement field,

(-\varepsilon \nabla\phi_{+})\cdot\nu_{+} 
+
(-\varepsilon \nabla\phi_{-})\cdot\nu_{-}
=
-Q

across the surface. Here $\nu{+,-}$ denote the outer normals to $\Omega{+,-}$. This is consistent with e.g. Dreyer et al, Eqn 27b (beware, $\nu$ therein denotes the outer normal of $\Omega_-$).

For $\varepsilon=1$ in 1D, the equation simplifies to

\phi_{+}'
-
\phi_{-}'
+
Q
=
0

See the solutions of the Example121 for homogeneous Dirichlet BCs for $Q>0$

and $Q<0$. The plots are consistent with the 1D equation above. However in breaction, the surface charge enters with - sign as -Q.