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Boundary Value Problems

, 2014:235

First Online: 07 November 2014Received: 03 September 2014Accepted: 20 October 2014

Abstract

In this paper, we describe a numerical method to verify the existence of solutions for a unilateral boundary value problems for second order equation governed by the variational inequalities. It is based on Nakao’s method by using finite element approximation and its explicit error estimates for the problem. Using the Riesz representation theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using Schauder fixed point theory, we construct a high efficiency numerical verification method that through numerical computation generates a bounded, closed, convex set which includes the approximate solution. Finally, a numerical example is illustrated.

MSC: 65G20, 65G30, 65N15, 65N30.

Keywordsnumerical verification error estimates variational inequalities unilateral boundary value problems for second order equations finite element method Schauder fixed point theory Electronic supplementary materialThe online version of this article doi:10.1186-s13661-014-0235-y contains supplementary material, which is available to authorized users.

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Autor: Cheon Seoung Ryoo

Fuente: https://link.springer.com/







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