Non-overlapping domain decomposition for the Richards equation via superposition operators

Abstract

Simulations of saturated-unsaturated groundwater flow in heterogeneous soil can be carried out by considering non-overlapping domain decomposition problems for the Richards equation in subdomains with homogeneous soil. By the application of different Kirchhoff transformations in the different subdomains local convex minimization problems can be obtained which are coupled via superposition operators on the interface between the subdomains. The purpose of this article is to provide a rigorous mathematical foundation for this reformulation in a weak sense. In particular, this involves an analysis of the Kirchhoff transformation as a superposition operator on Sobolev and trace spaces.