MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Efficient Inversion of the Galerkin Matrix of General Second Order Elliptic Operators with Non-Smooth Coefficients

Mario Bebendorf


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.

MSC Codes:
35C20, 65F05, 65F50

Related publications

2005 Repository Open Access
Mario Bebendorf

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

In: Mathematics of computation, 74 (2005) 251, pp. 1179-1199