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In this paper we propose and analyze a preconditioner for a system arisingfrom a finite element approximation of second order elliptic problemsdescribing processes in highly het- erogeneous media. Our approach uses thetechnique of multilevel methods and the recently proposed preconditioner basedon additive Schur complement approximation by J. Kraus (see [8]). The mainresults are the design and a theoretical and numerical justification of aniterative method for such problems that is robust with respect to the contrastof the media, defined as the ratio between the maximum and minimum values ofthe coefficient (related to the permeability/conductivity).

Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media