A numerical upscaling method for an elliptic equation with heterogeneous tensorial coefficients

The aim of this paper is to develop a new numerical method to determine the e ective permeability on a coarse scale level of problems with strongly heterogeneous tensorial coe cients de ned on a ne scale. This method stems from a primal–dual mixed formulation and the upscaled permeability is obtained by imposing the continuity of the numerical ux across the lines of discontinuities. Moreover, a nite volume scheme is built to numerically solve elliptic equations with this kind of coe cients. Finally, the method is illustrated by several numerical experiments