Numerical verification of solutions for Signorini problems using Newton‐like method
Cheon Seoung Ryoo · International Journal for Numerical Methods in Engineering · 2007
Abstract We proposed a numerical method to verify the existence of solutions for a simplified Signorini problem (Comput. Math. Appl. 2000; 40:1003–1013). Using sequential iteration method, we numerically constructed a set containing solutions that satisfies the hypothesis of Schauder's fixed point theorem in a certain Sobolev space. It is difficult to apply this method to the problem of which associated operator is not retractive in a neighborhood of the solution. In this paper, in order to overcome such a difficulty, we describe an alternative approach to this problem. Numerical examples are presented. Copyright © 2007 John Wiley & Sons, Ltd.