  Matlab Database > Partial Differential Equations > Finite Element Method > Obstacle problem in 1D with penalty

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 Title: Obstacle problem in 1D with penalty Author: Stefan Hueeber E-Mail: hueeber-AT-ians.uni-stuttgart.de Institution: University of Stuttgart Description: This program solves the 1D obstacle problem -w" >= q/S w >= g (w" + q/S)(w - g) = 0 on the interval (0,laenge) for homogeneous Dirichlet boundary conditions: w(0) = w(laenge) = 0. The right hand side is given by an area load q and a traction force S. The solution is performed by a penalty method which arises from the variational problem of the second kind. Three different implementations for the discretisation of the indicator function are considered: 1. \chi_eps = eps/2*sum_i (min(0,w_i-g_i)^2) (i=nodes) 2. \chi_eps = eps/2*sum_e |min(0,w-g)|_{0,e})^2 (e=element) 3. \chi_eps = eps/4*sum_i (min(0,w_i-g_i)^4) (i=nodes) In the first and the third case the condition (w>= g) is only penalized at the discretization nodes. Therefore the konvex set K of the admissible functions w is replaced by a discrete set K_h given by the polygon thhrough the discretization nodes. In the second case even in the discretization the origin continuous set K is used (due to the penelization by the L2-norm). Start the program with the command penalty and Choose the paramters in the file penalty.m. Keywords: obstacle probelm 1D, variational inequality of first kind, penalty method File Name: pen2K.zip File Size: 3 KB File Version: 1.0 Matlab Version: 7.0 (R14) Date: 2007-05-24 Downloads: 2013 Download File  © Technische Universität München 2011 | Disclaimer | Impressum Rechtshinweise