  We study the question of approximability for the inverse of the FEM stiffness
matrix for (scalar) second order elliptic boundary value problems by blockwise
low rank matrices such as those given by the H-matrix format. We show that
exponential convergence in the local block rank can be achieved. We also show
that exponentially accurate LU-decompositions in the H-matrix format are
possible for the stiffness matrices arising in the FEM. Unlike prior works, our
analysis avoids any coupling of the block rank r and the mesh width h and also
covers mixed Dirichlet-Neumann-Robin boundary conditions.
