Some iterative algorithms for the obstacle problems

Abstract

In this paper we propose some iterative algorithms for the obstacle problems discretized by the finite difference method. We rewrite the obstacle problem to an equivalent complementarity problem. We use the regularization trick to non-smooth absolute function. Then we apply the Newton's method to obtain an iterative algorithm. Some other two algorithms based on this algorithm are derived. Numerical experiments show the effective of the algorithm.

Keywords:

• obstacle problem
• iterative algorithm
• complementarity problem
• finite difference
• monotone iteration

2000 AMS Subject Classifications :

• 65N06
• 65F10
• 90C33
• 65N22
• 65N12

Acknowledgements

The work was supported by National Natural Science Foundation of China (Grant No. 10471129) and Zhejiang Province Natural Science Foundation of China (Grant No. Y607504).