TITLE:
A Cubic Spline Method for Solving a Unilateral Obstacle Problem
AUTHORS:
El Bekkey Mermri, Abdelhafid Serghini, Abdelmajid El hajaji, Khalid Hilal
KEYWORDS:
Obstacle Problem; Spline Collocation; Nonsmooth Equation; Generalized Newton Method
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.2 No.3,
September
28,
2012
ABSTRACT: This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-ship between the penalty parameter and the discretization parameter h is satisfied. An error estimate between the penalty solution and the discret penalty solution is provided. To validate the theoretical results, some numerical tests on one dimensional obstacle problem are presented.