Iterative methods and parallel solution of the dam problem Original Research Article

A free boundary problem of fluid flow in the porous medium is considered. A finite difference scheme is constructed and written in the form of the inclusion for the sum of several multi-valued operators. The study of this mesh scheme and iterative algorithms of its numerical solution is performed. Solution of the mesh problem by Gauss–Seidel and by Schwarz alternating methods was executed. The numerical results are reported which confirm the theoretical results.