Analysis of a Coupled Darcy Multiple Scale Flow Model Under Geometric Perturbations of the Interface

Abstract

For a Darcy flow coupled system modeling fluid exchange between two regions with fluid resistance at different scale, we address the question of continuity of the solution with respect to geometric perturbations of the interface. The original interface and its perturbation define three flow regions exchanging fluid, these are modeled as a coupled system in mixed variational formulation. For numerical purposes a-posteriori perturbation/error estimates are given.