A COMPUTATIONAL VERIFICATION METHOD OF SOLUTION WITH UNIQUENESS FOR OBSTACLE PROBLEMS

@article{Ryoo1998ACV,
  title={A COMPUTATIONAL VERIFICATION METHOD OF SOLUTION WITH UNIQUENESS FOR OBSTACLE PROBLEMS},
  author={Cheon Seoung Ryoo},
  journal={Bulletin of informatics and cybernetics},
  year={1998},
  volume={30},
  pages={133-144}
}
  • C. Ryoo
  • Published 1 March 1998
  • Mathematics
  • Bulletin of informatics and cybernetics
A numerical method for automatic proof of the existence of solutions for variational inequalities is proposed. It is based on the infinite di mensional fixed point theorem and computable error estimates for finite element approximations of the original problems. Particularly, in this paper, we consider the method to prove the uniqueness of solution for obstacle problem. Further, some numerical examples are presented. In the author's previous work (Ryoo and Nakao (1998)), we proposed a numerical… 
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References

SHOWING 1-10 OF 11 REFERENCES

A numerical approach to the proof of existence of solutions for elliptic problems

In this paper, we describe a method which proves by computers the existence of weak solutions for linear elliptic boundary value problems of second order. It is shown that we can constitute the

A numerical approach to the proof of existence of solutions for elliptic problems II

This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder’s fixed point theorem, of the existence of weak solutions for

Numerical verification of solutions for variational inequalities

TLDR
Using the finite element approximations and explicit a priori error estimates for obstacle problems, an effective verification procedure is presented that through numerical computation generates a set which includes the exact solution.

Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anL∞Residual Method☆

Abstract We consider a numerical enclosure method with guaranteedL∞error bounds for the solution of nonlinear elliptic problems of second order. By using an a posteriori error estimate for the

Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

SummaryIn this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary

Numerical Methods for Nonlinear Variational Problems

Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the

Nonlinear Programming