Numerical solving of stationary anisotropic filtration problems

The paper is devoted to the methods of numerical solving of stationary filtration problems of non-compressible fluid following the nonlinear multi-valued anisotropic filtration law with limiting gradient. This problem is mathematically formulated in the form of variational inequality of the second kind in Hilbert space with inversely strongly monotone operator. The functional occurring in this variational inequality is a sum of several lower semi-continuous convex proper functionals. For the solution of the considered variational inequality the splitting method is offered. This method allows finding both the pressure and the filtration velocity. The results of numerical experiments are presented.