Solving the nonstationary Richards equation with adaptive hp-FEM

Abstract

This paper examines the potential of the adaptive hp-FEM method for the numerical solution of time-dependent variably saturated Darcian flow problems described by the Richards equation. The method is illustrated on three model problems: a benchmark with known exact solution, groundwater seepage into a dry lysimeter box with time-dependent boundary conditions, and capillary barrier behavior under an intense infiltration. In the second part of the paper we present the weak formulation of the Richards equation for the Newton’s and Picard’s methods, give a brief overview of adaptive hp-FEM with emphasis on aspects that are usually not discussed in the literature, and we briefly introduce the open source adaptive hp-FEM library HERMES that was used to generate numerical results for this paper. All computations that we present are easily reproducible.