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

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