Iterative methods and parallel solution of the dam problem

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. © 2001 Elsevier Science B.V. All rights reserved