FIRST-ORDER SYSTEM LEAST SQUARES FOR SECOND-ORDER
                   PARTIAL DIFFERENTIAL EQUATIONS:  PART I

                                    Z. Cai
                                  R. Lazarov
                               T. A. Manteuffel
                               S. F. McCormick

                                   Abstract

This paper develops ellipticity estimates and discretization error bounds for
elliptic equations (with lower order terms) that are reformulated as a
least-squares problem for an equivalent first-order system.  The main result
is the proof of ellipticity, which is used in a companion paper to establish
optimal convergence of multiplicative and additive solvers of the discrete
systems.