\Omega,
    \end{cases}$$ where $\Omega$ is a bounded subset of $\R^d$ (of arbitrary dimension $d\in \mathbb{N}^*$) with piecewise Lipschitz boundary, $a$ is a symmetric, uniformly elliptic $d\times d$ matrix with entries in $L^\infty(\Omega)$ and such that for all $x\in \Omega$ and $l\in \R^d$, $$\lambda_{\min}(a) |l|^2 \leq l^T a(x) l \leq \lambda_{\max}(a)|l|^2.$$ Although multigrid methods [@Fedorenko:1961; @Brandt:1973; @Hackbusch:1978; @Hackbusch:1985; @Stuben:2001] are now well known as the fastest for solving elliptic boundary-problems and have successfully been generalized to other types of PDEs and computational problems [@Yavneh:2006], their convergence rate can be severely affected by the lack of regularity of the coefficients [@EngquistLuo:1997; @wan2000]. Furthermore, although significant progress has been achieved in the development of multigrid methods that are, to some degree, robust with respect to meshsize and lack of smoothness (we refer in particular to algebraic multigrid [@RugeStuben1987], multilevel finite element splitting [@Yserentant1986], hierarchical basis multigrid [@BankYserentant88; @ChowVassilevski2003], multilevel preconditioning [@Vassilevski89], stabilized hierarchical basis methods [@Vassilevski1997sirev; @VassilevskiWang1997a; @VassilevskiWang1998], energy minimization [@Mandel1999; @wan2000; @Xu2004; @XuZhu2008; @Vassilevski2010] and homogenization based methods [@EngquistLuo:1997; @Efendiev2011]), the design of multigrid methods that are provably robust with respect to rough ($L^\infty$) coefficients has remained an open problem of practical importance [@BraWu09].

Alternative hierarchical strategies for the resolution of are 