Time-space finite elements for unsaturated flow through porous media

Abstract

In this paper one-dimensional unsaturated flow problems are solved by time-space elements based on three different formulations (quasi-variational, least square and least square collocation). A family of isoparametric two-dimensional elements is developed based on all three approaches, while for the latter two formulations, elements with slope continuity in space are also used because of continuity requirements. The results for a number of examples are compared and it is concluded that the quasi-variational method produces the most accurate results and requires the least amount of computer time. Refs.