A MULTISCALE FINITE DIFFERENCE METHOD FOR LINEAR ELLIPTIC PROBLEMS IN HETEROGENEOUS MEDIA
Alexandre Santos Francisco, Jorge Juárez Trujillo, Leonardo Menezes Sacramento · 2016
We present a multiscale finite difference method to solve problems of highly heterogeneous porous medium flow. Heterogeneity in permeability fields is assumed to occur on a wide range of length scales. Our multiscale method allows for incorporating fine-scale information of the permeability into coarse-scale iteration procedures. In this direction, we define multiscale basis functions in order to obtain discrete solutions in local problems. In another paper, such basis functions have already been defined by using hybridized mixed finite elements. In this paper, we use finite differences to do so. Our multiscale method is expected to be an inexpensive alternative to solve the global problem at only fine scale. Numerical results are presented to check the performance of the multiscale method