AN ENCLOSURE METHOD FOR FREE BOUNDARY PROBLEMS BASED ON A LINEAR COMPLEMENTARITY PROBLEM WITH INTERVAL DATA^*

Abstract

This paper presents the linear complementarity problem with interval data and emphasizes its application in including the solution of an ordinary free boundary problem. This study is based on Taylor's formula with remainder and the reformulation of linear complementarity problems as nonsmooth nonlinear systems of equations.

^*This paper contains to some extent results from the author's Ph.D. thesis [1].

Keywords:

• Linear complementarity problems
• Free boundary problems
• Enclosure methods
• Interval computations
• AMS Subject Classifications: 90C33; 65L10; 65G20

ACKNOWLEDGMENT

The author would like to thank the referees for their helpful comments.

Notes

^*This paper contains to some extent results from the author's Ph.D. thesis [1].

In [13] a sequence of ordinary free boundary problems arises by discretizing a parabolic free boundary problem with respect to the time variable.

In [3] the continuity of G(x, y, q, M) in y ∈ [z] is not needed, since the authors were using a generalized Krawczyk operator