A new numerical approach to a non-steady filtration problem

A free-boundary transient problem of seepage flow is studied from a numerical standpoint. From a suitable formulation of the problem in terms of variational inequality we introduce a new numerical approach of the implicit type and based on the finite element method. In this approach the problem is solved on a fixed region and the position of the free boundary is automatically found as part of the solution of the problem; so it is not necessary to solve a succession of problems with different positions of the free boundary. We prove stability and convergence for the approximate solution and we give several numerical results. Work supported by C. N. R. of Italy through the Laboratorio di Analisi Numerica of Pavia.