<P>
In all the cases just listed, it is the evaluation of a functional <I>J</I>(<I>u</I>) of
-the solution which we are interested in, rather than the values of <I>u</I>everywhere. Since the exact solution <I>u</I> is not available, but only its
+the solution which we are interested in, rather than the values of <I>u</I> everywhere. Since the exact solution <I>u</I> is not available, but only its
numerical approximation <I>u</I><SUB><I>h</I></SUB>, it is sensible to ask whether the computed
value <I>J</I>(<I>u</I><SUB><I>h</I></SUB>) is within certain limits of the exact value <I>J</I>(<I>u</I>), i.e. we
want to bound the error with respect to this functional,
<BR>Adaptive discontinuous Galerkin finite element methods for
nonlinear hyperbolic conservation laws.
<BR>Preprint 2001-20, (SFB 359), IWR Heidelberg, Mai 2001.
-<BR>submitted.
+<BR>to appear in SIAM J. Sci. Comp.
<P>
<P></P><DT><A NAME="HH01b"><STRONG>13</STRONG></A>