This article is cited in 1 paper

On convergence of the explicit difference scheme for evolution variational inequality with nonlocal space operator

O. V. Glazyrina, M. F. Pavlova

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: Nonlinear parabolic variational inequality with a nonlocal space operator monotone with respect to the gradient is considered. Using the methods of penalty and summatory identities, explicit difference scheme with respect to the space operator and implicit difference scheme with respect to the penalty operator are constructed. Conditions of stability for the constructed difference scheme are obtained. The theorem of convergence is proved under minimal assumptions on the smoothness of the original data.

Keywords: variational inequality, operator monotone with respect to gradient, nonlocal operator, explicit difference scheme with penalty operator, stability, convergence.

UDC: 519.6

Received: 30.07.2015

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