Iterative method for solving seepage problems in multilayer beds in the presence of a point source

The paper is devoted to solving the stationary seepage problems of non-compressible fluid following the nonlinear multi-valued filtration law with limiting gradient in multilayer beds in the presence of a point source. This problem is mathematically formulated in the form of mixed variational inequality with inversely strongly monotone operator in Hilbert space. For the solving of the considered variational inequality the iterative splitting method is offered. Unlike the previously considered methods, this one makes it possible to find not only the pressure of the fluid, but also the filtration velocity in the domains corresponding to the multi-valued points in the filtration law. The convergence of the iterative method results is investigated.