Numerical solution of Variational Inequalities by Adaptive Finite Elements
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Advances in Numerical Mathematics
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Sprache:Englisch
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Erscheinungsdatum
12.03.2009
Verlag
Vieweg+TeubnerSeitenzahl
161 (Printausgabe)
Dateigröße
6570 KB
Sprache
Englisch
EAN
9783834895462
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.
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.
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