  We present a hybridization technique for summation-by-parts finite difference
methods with weak enforcement of interface and boundary conditions for second
order, linear elliptic partial differential equations. The method is based on
techniques from the hybridized discontinuous Galerkin literature where local
and global problems are defined for the volume and trace grid points,
respectively. By using a Schur complement technique the volume points can be
eliminated, which drastically reduces the system size. We derive both the local
and global problems, and show that the linear systems that must be solved are
symmetric positive definite. The theoretical stability results are confirmed
with numerical experiments as is the accuracy of the method.
