%%%%%%%%title of contribution
\Atitle{Some Remarks on A Posteriori Finite Element Error Analysis  and DWR}

%%%%%%%%name of authors connected by "and"
\Aauthor{\underline{C. Carstensen}}

%%%%%%%%abbreviation of authors names for running header
\renewcommand{\rauthor}{C. Carstensen}

%%%%%%%affiliations and e-mail
\Aaddress{%
Humboldt-Universit{\"a}t zu Berlin, \quad{\tt cc@math.hu-berlin.de}}

%%%%%%%please enter some keywords describing your contribution
%\Akeywords{some keywords}

%%%%%%%abstract of contribution
\Aabstract{%
The overwhelming success of  Heidelberg's Dual Weighted
Residual (DWR)
Technology is essentially based on striking numerical evidence. The
theoretical
justification appears less clear in the sense that the best known
post-processing
algorithms are employed to approximate the unknown exact dual solution $z$
and/or its higher derivatives. All the information is utilised to
compute and perhaps
nothing left for strict error control.

The presentation discusses three different versions of the DWR and
studies them
numerically for a simple Poisson model equation followed by eigenvalue
problems
and ends with an outlook for nonlinear minimisation problems.
}

%A list of references might be at the end of the abstract.  When referring to
%them in the text, type the corresponding reference number
%between brackets \cite{dieu3}.  References should be given in the standard
%style as follows.