\qquad\qquad u(0)=0,
\quad u(1)=1.
\end{equation}
-Note that this equation degenerates whereever $u^3=x$, which is at least the
+Note that this equation degenerates wherever $u^3=x$, which is at least the
case at $x\in\{0,1\}$ due to the prescribed boundary values for $u$, but
possibly at other places as well. However, for finite elements, we will want
to have the equation in weak form anyway. Since the equation is still
the internal consistency of the library. The library contains several
thousands of these checks, and they significantly slow down debug
computations, but we feel that the benefit of finding programming errors
-earlier and including where the problem exactly appeared to be of signicantly
+earlier and including where the problem exactly appeared to be of significantly
greater value than faster run-time. After all, all production runs of programs
should be done in optimized mode anyway.