First-Order System Least Squares for Second-Order
Partial Differential Equations: Part I

Z. Cai
Department of Mathematics
University of Southern California
1042 W. 36th Place
Los Angeles, CA 90089-1113

R. Lazarov
Department of Mathematics
Texas A&M University
College Station, TX 77843--3368

T. A. Manteuffel and S. F. McCormick
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.