Numerical solution of Variational Inequalities by Adaptive Finite Elements
Suttmeier, Franz-Theo
Numerical solution of Variational Inequalities by Adaptive Finite Elements [electronic resource]/ by Franz-Theo Suttmeier. - Wiesbaden: Vieweg+Teubner Verlag, 2008. - X, 161p. 51 illus., 10 illus. in color. digital.
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 .
9783834895462
10.1007/978-3-8348-9546-2 doi
Mathematics
510
Numerical solution of Variational Inequalities by Adaptive Finite Elements [electronic resource]/ by Franz-Theo Suttmeier. - Wiesbaden: Vieweg+Teubner Verlag, 2008. - X, 161p. 51 illus., 10 illus. in color. digital.
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 .
9783834895462
10.1007/978-3-8348-9546-2 doi
Mathematics
510