A Convergence of an Implicit Difference Scheme for the Saturated-Unsaturated Filtration Consolidation Problem

An implicit difference scheme for the problem of saturated-unsaturated filtration consolidation is considered and analyzed under the condition when a part of the boundary is semipermeable. The penalty method is applied to establish the existence of a solution to the difference problem. The convergence of the difference scheme is studied under minimal assumptions on the smoothness of the original data: the convergence of the piecewise-constant extensions of the difference solution to the generalized solution of the problem is proved.