TY - JOUR
T1 - A Level Set Method for Solving Free Boundary Problems Associated with Obstacles
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 157
EP - 172
PY - 2004
DA - 2004/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/972.html
KW - Level set methods, free boundary problems, obstacle problem.
AB - <p style="text-align: justify;">A level set method is proposed for solving free boundary problems
coming from contact with obstacles. Two different approaches are described and
applied for solving a unilateral obstacle problem. The cost functionals coming
from the new approach are nonsmooth. For solving the nonsmooth minimization
problems, two methods are applied: firstly, a proximal bundle method,
which is a method for solving general nonsmooth optimization problems. Secondly,
a gradient method is proposed for solving the regularized problems.
Numerical experiments are included to verify the convergence of the methods
and the quality of the results.</p>