Beschreibung:
We investigate the problem of computing the inverses of stiffness matrices resulting from the finite element discretization of elliptic partial differential equations. Since the solution operators are non-local, the inverse matrices will in general be dense, therefore they cannot be represented by standard techniques. In this paper, we prove that these matrices can be approximated by - and -matrices. The key results are existence proofs for local low-rank approximations of the solution operator and its discrete counterpart, which give rise to error estimates for H- and H2-matrix approximations of the entire matrices.