quantity. From extrapolating it, we can guess that the exact value is
somewhat like 0.0334473, plus or minus 0.0000001 (note that we get
almost 6 valid digits from only 22,000 (primal) degrees of
-freedom. This number cannot be obtaint from the value of the
+freedom. This number cannot be obtained from the value of the
functional alone, but I have used the assumption that the error
estimator is mostly exact, and extrapolated the computed value plus
the estimated error, to get an approximation of the true
, 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
-nonlinear, one may be tempted to we compute iterates
+nonlinear, one may be tempted to compute iterates
<!-- MATH
$u_{k+1}=u_k+\alpha_k\delta u_k$
-->
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
-nonlinear, one may be tempted to we compute iterates
+nonlinear, one may be tempted to compute iterates
$u_{k+1}=u_k+\alpha_k\delta u_k$ using a Newton method for updates $\delta
u_k$, like in
\begin{equation*}
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