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A method of successive approximations for solving the quasi-variational Signorini inequality

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Abstract

We solve the semicoercive quasi-variational Signorini inequality that corresponds to the contact problem with friction known in the elasticity theory by a method of successive approximations. For solving auxiliary problems with a given friction occurring on each outer step of the iterative process we use the Uzawa method based on iterative proximal regularization of a modified Lagrangian functional. We study the stabilization of the sequence of auxiliary finite-element solutions obtained on outer steps of the method of successive approximations and present results of numerical calculations.

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Authors and Affiliations

  1. Computing Center of Far-Eastern Branch of Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000, Russia

    R. V. Namm & G. I. Tsoi

Authors
  1. R. V. Namm
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  2. G. I. Tsoi
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Correspondence to R. V. Namm.

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Original Russian Text © R.V. Namm and G.I. Tsoi, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 1, pp. 44–52.

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Namm, R.V., Tsoi, G.I. A method of successive approximations for solving the quasi-variational Signorini inequality. Russ Math. 61, 39–46 (2017). https://doi.org/10.3103/S1066369X17010054

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