  We present a method for the distributed finite element solution of elliptic
boundary value problems using model order reduction on each subdomain of the
domain decomposition. We show that the error of the reduction can be
succesfully controlled in the $H^1$ norm due to the properly weighted $l^2$
low-rank approximation. Our numerical results demonstrate the technique using
tetrahedral meshes with up to 85 million degrees-of-freedom on a laptop
computer by distributing the bulk of the model order reduction to the cloud.
