WIDTH="112" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="step-11.data/img4.gif"
ALT="$H^1(\Omega)\subset L^1(\Omega)$">
-by Sobolev's inequality, and thus also on the continuous level since we
+by Sobolev's inequality, and thus also on the discrete level since we
there only consider subsets of <I>H</I><SUP>1</SUP>.
<LI>Fixing the mean value over the boundary of the domain to zero or any
other value. This is also allowed on the continuous level, since
\item Fixing the mean value over the domain to zero or any other value. This
is allowed on the continuous level, since $H^1(\Omega)\subset L^1(\Omega)$
- by Sobolev's inequality, and thus also on the continuous level since we
+ by Sobolev's inequality, and thus also on the discrete level since we
there only consider subsets of $H^1$.
\item Fixing the mean value over the boundary of the domain to zero or any
As we expected, the convergence order for each of the different
mappings is clearly quadratic in the mesh size. What <it>is</it>
interesting, though, is that the error for a bilinear mapping
-(i.e. degree 1) is more that three times larger than that for the
+(i.e. degree 1) is more than three times larger than that for the
higher order mappings; it is therefore clearly advantageous in this
case to use a higher order mapping, not because it improves the order
of convergence but just to reduce the constant before the convergence
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