Title: 
Obstacle problem in 1D with penalty

Author: 
Stefan Hueeber 
EMail: 
hueeberATians.unistuttgart.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_ig_i)^2) (i=nodes)
2. \chi_eps = eps/2*sum_e min(0,wg)_{0,e})^2 (e=element)
3. \chi_eps = eps/4*sum_i (min(0,w_ig_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 L2norm).
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:  20070524 
Downloads:  1705 
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