Numerical Solution of Variational Inequalities by Adaptive Finite Elements

By Franz-Theo Suttmeier

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.

• Format: Paperback
• Language: English
• ISBN: 3834806641
• ISBN13: 9783834806642
• Release Date: August 2008
• Publisher: Vieweg+teubner Verlag
• Length: 161 Pages
• Weight: 0.47 lbs.
• Dimensions: 0.4" x 5.8" x 8.3"