Partial Differential Equations: Part I

Department of Mathematics

University of Southern California

1042 W. 36th Place

DRB-155

Los Angeles, CA 90089-1113

Department of Mathematics

Texas A&M University

College Station, TX 77843--3368

Program in Applied Mathematics

Campus Box 526

University of Colorado at Boulder

Boulder, CO 80309-0526

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.

Contributed April 24, 1995.