On the convergence of an approximate method for solving the problem filtration consolidation with a limiting gradient

Abstract

A one-dimensional initial-boundary value problem modelling the process of joint motion of a viscoelastic porous medium and a liquid saturating the medium is considered. In the filtration theory, this process is called filtration consolidation. A finite element in spatial variable and time-implicit difference scheme is constructed. Its solvability is established, the convergence piecewise-constant filling of an approximate solution in the variable t to generalized solution of problem is proved.