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

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.