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Franz-Theo Suttmeier describes a general approach to a posteriori error estimation
and adaptive mesh design for finite element models where the solution
is subjected to inequality constraints. This is an extension to variational
inequalities of the so-called Dual-Weighted-Residual method (DWR method)
which is based on a variational formulation of the problem and uses global
duality arguments for deriving weighted a posteriori error estimates with respect
to arbitrary functionals of the error. In these estimates local residuals of
the computed solution are multiplied by sensitivity factors which are obtained
from a numerically computed dual solution. The resulting local error indicators
are used in a feed-back process for generating economical meshes which
are tailored according to the particular goal of the computation. This method
is developed here for several model problems. Based on these examples, a general
concept is proposed, which provides a systematic way of adaptive error
control for problems stated in form of variational inequalities.
Models in elasto-plasticity.- The dual-weighted-residual method.- Extensions to stabilised schemes.- Obstacle problem.- Signorini’s problem.- Strang’s problem.- General concept.- Lagrangian formalism.- Obstacle problem revisited.- Variational inequalities of second kind.- Time-dependent problems.- Applications.- Iterative Algorithms.- Conclusion.