Localization of Multiscale Screened Poisson Equation
Viktor Bäck · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2012
In this paper we investigate a local fine scale problem which arises in various 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 equation, and state a Proposition in which we get a theoretical bound of the decay. Furthermore we present extensive numerical tests which confirms our theoretical 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. ∗Department of Information Technology, Uppsala University, Box 337 SE-751 05 Uppsala, Sweden †Supervisor: Axel Malqvist