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
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:
File Size: 3 KB
File Version: 1.0
Matlab Version: 7.0 (R14)
Date: 2007-05-24
Downloads: 2013
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