Localization of Multiscale Screened Poisson Equation

In this paper we investigate a local fine scale problem which arises in var-ious multiscale methods, see e.g. [1]. Local fine scale problems are solved and used to modify coarse scale basis functions. We analyze the decay of these basis functions in the case of localization of the screened Poisson equa-tion, and state a Proposition in which we get a theoretical bound of the decay. Furthermore we present extensive numerical tests which confirms our the-oretical results. The screened Poisson equation can be view as a temporal discrete parabolic equation, and can be used to model time-dependent flow in porous media