This article is cited in 1 paper

Effectively implementable iterative methods for the linear elliptic variational inequalities with constraints to the gradient of solution

N. S. Kashtanov, A. V. Lapin

Chair of Mathematical Statistics, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We construct and investigate a new iterative method for a finite dimensional constrained saddle point problem. The obtained results are applied to prove the convergence of different iterative methods for the mesh approximations of variational inequalities with constraints to the gradient of a solution. In particular, we prove the convergence of two-stage iterative methods. The main advantage of the proposed methods is the simplicity of their implementation. The results of the numerical testing demonstrate high convergence rate.

Keywords: saddle point problem with constraints, variational inequality, finite difference approximation, iterative methods.

UDC: 519.6

Received: 21.01.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:7, 7–20

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