A Discontinuous Hybrid Mixed Formulation for the 2D Multiscale Porous Media Flow Problem

Abstract

In this paper a new hybrid finite element method is introduced, aimed to model multiscale problems with several geometric regions of the domain of interest. In each of these regions porous media fluid flow takes place, but governed by physical parameters at a different scale; additionally, a fluid exchange through contact interfaces occurs between neighboring regions. The well-posedness of the hybrid finite element formulation on bounded simply connected polygonal domains of the plane is presented. Next, the convergence of the discrete solution to the exact solution of the problem is discussed. Finally, the numerical example illustrates the method and experimental rates of convergence.