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Numerical verification of solutions for variational inequalities

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Abstract.

In this paper, we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities. This technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations. Using the finite element approximations and explicit a priori error estimates for obstacle problems, we present an effective verification procedure that through numerical computation generates a set which includes the exact solution. Further, a numerical example for an obstacle problem is presented.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University 33, Fukuoka 812–81, Japan; e-mail:ryoo@math.kyushu-u.ac.jp; e-mail: mtnakao@math.kyushu-u.ac.jp , , , , , , JP

    Cheon Seoung Ryoo & Mitsuhiro T. Nakao

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  1. Cheon Seoung Ryoo
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  2. Mitsuhiro T. Nakao
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Received October 28,1996 / Revised version received December 29,1997

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Ryoo, C., Nakao, M. Numerical verification of solutions for variational inequalities. Numer. Math. 81, 305–320 (1998). https://doi.org/10.1007/s002110050394

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  • DOI: https://doi.org/10.1007/s002110050394

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