A RIGOROUSLY JUSTIFIED ROBUST ALGEBRAIC PRECONDITIONER FOR HIGH-CONTRAST DIFFUSION PROBLEMS

In this paper we analyse the robustness of (algebraic) multigrid preconditioners applied to linear systems arising from finite element approximations of elliptic PDEs with high-contrast coefficients. Problems with high-contrast coefficients are ubiquitous in porous media flow applications. Consequently, development of efficient solvers for high-contrast heterogeneous media has been an active area of research. Here we are particularly concerned with the convergence of a family of algebraic preconditioners that exploit the binary character of high-contrast coefficients (see also [1]).