# Институт вычислительной математики

и математической геофизики

# The International Conference on Computational Mathematics

ICCM-2004

June, 21-25, 2004
Novosibirsk, Academgorodok

## Abstracts

*Numerical solution of differential and integral equations*

## On the numerical solution of the some nonlinear the seepage theory problems.

**Kazan State University (Kazan)**

We study variational inequalities of the second kind with a pseudomonotone operator and convex non-differentiable functional in Banach spaces that occur, in particular, during the description of the stationary seepage processes. For variational inequality solving a two-level method of iterative regularization is suggested. It allows to reduce the solution of the original variational inequality and the regularized functional to the solution of the variational inequality with the duality operator. Duality operator has better properties compared to the original operator. We investigate the convergence of an iterative process. It is proved that the iterative sequence is bounded, any of its weak limit points are a solutions of the original inequality. In the case of a Hilbert space under the additional limitation the weak convergence of the whole iterative sequence is proved. The method suggested in this report leads to the essentially easier problem (in the sense of its implementation) if the regularized functional becomes differentiable. The numerical experiments are carried out.

*Note. Abstracts are published in author's edition*

© 1996-2000, Siberian Branch of Russian Academy of Sciences, Novosibirsk

Last update: 06-Jul-2012 (11:52:06)