Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients

Abstract

This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with $L^\infty$-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices ($\mathcal {H}$-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity.