ABSTRACT 
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 nonlocal, 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 H and H2matrices. 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 H2matrix approximations of
the entire matrices.
