Dimensional Reduction by Fourier Analysis of a Stokes-Darcy Fracture Model

We consider a Stokes flow along a thin fracture coupled to a Darcy flow in the surrounding matrix domain. In order to derive a dimensionally reduced model representing the fracture as an interface coupled to the surrounding matrix, we extend the methodology based on Fourier analysis developed in [1] for a Darcy-Darcy coupling. We show that this approach not only allows us to derive error estimates between the solutions of the full and mixed-dimensional models, but also leads to a model correction term compared with what is obtained from the classical reduction technique based on integration along the fracture width combined with profile closure assumptions [2, 3].