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

Johannes Kraus, Raytcho Lazarov, Maria Lymbery, Svetozar Margenov, Ludmil Zikatanov

Published 2014-06-17, updated 2014-12-01Version 3

In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of multilevel methods and the recently proposed preconditioner based on additive Schur complement approximation by J. Kraus (see [8]). The main results are the design and a theoretical and numerical justification of an iterative method for such problems that is robust with respect to the contrast of the media, defined as the ratio between the maximum and minimum values of the coefficient (related to the permeability/conductivity).