TY  - BOOK
AU  - Suttmeier,Franz-Theo
ED  - SpringerLink (Online service)
TI  - Numerical solution of Variational Inequalities by Adaptive Finite Elements
SN  - 9783834895462
AV  - QA297-299.4 
U1  - 518 23
PY  - 2008///
CY  - Wiesbaden
PB  - Vieweg+Teubner
KW  - Mathematics
KW  - Numerical analysis
KW  - Numerical Analysis
KW  - Mathematics, general
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-8348-9546-2
ER  -