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Numerical Solution of Variational Inequalities by Adaptive Finite Elements
Paperback
Series: Advances in Numerical Mathematics
ISBN13: 9783834806642
Publisher: Vieweg+teubner Verlag
Published: Aug 28 2008
Pages: 161
Weight: 0.47
Height: 0.37 Width: 5.83 Depth: 8.27
Language: English
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),
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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