\documentstyle{article}
\parskip 3ex
\parindent 0pt
\pagestyle{empty}
\begin{document}
\begin{center}
{\bf A posteriori Error Estimates and Adaptivity for Linear Elastic Plate
Deformation and Problems of Linear Viscoelasticity}
\end{center}

\begin{center}
Marcus Ludwig, Simon Shaw and J R Whiteman.
\end{center}

\begin{center}
BICOM, Institute of Computational Mathematics,
Brunel University, Uxbridge, Middlesex, UK.
\end{center}

Mathematical models involving first-order shear deformation of thick
elastic plates and of linear viscoelastic solid deformation involving
history integral formulations are first presented. Discretisations
of the plate model using Galerkin finite element techniques with piecewise
bilinear approximating functions on quadrilateral partitions and of the
viscoelastic deformation using space/time Galerkin finite element methods
are then proposed.

The machinery of Johnson et al., which exploits Galerkin orthogonality,
properties of the approximating functions, dual problems and the stability
of the solutions, for deriving a posteriori error estimates is then
described. These error estimates involve constants and are thus only of
practical use if these constants can be bounded or approximated.

This machinery is then applied to the above plate models and
discretisations and a posteriori error estimates with calculated values
for all the relevant constants are produced, together with resulting
adapted meshes arising when transition elements and irregular midside
nodes are employed.

For the problems of linear viscoelasticity the machinery is again used
and a posteriori error estimates for the space/time finite element
approximations are produced and their dependence on assumptions made in
the formulation of the models of viscoelasticity is explained.
\end{document}